Contents

#Loading required packages
library(Statial)
library(tidyverse)
library(plotly)

theme_set(theme_classic())

1 Installation

# Install the development version from GitHub:
# install.packages("devtools")
devtools::install_github("SydneyBioX/Statial")

2 Overview

Konditional is a method to evaluate the localisation relationship between two cell types in an image. Konditional builds on the L-function by contenualising the relationship between two cell types in reference to the typical spatial behaviour of a \(3^{rd}\) cell type/population. By taking this approach, Konditional is invariant to changes in the window of the image as well as tissue structures which may be present.

3 Loading example data

In the following we will analyse some Head and Neck cancer data. These images are stored in a SingleCellExperiment object. The first step in analysing these images is to organise all the cells present into cell populations, e.g. all the B cells are put in a vector called bcells.

# Load head and neck data
#data("headSCE")
load("../data/headSCE.rda")


# Examine all cell types in image
unique(headSCE$cellType)
#>  [1] EC1       SC7       MC3       Undefined BC3       SC1       SC2      
#>  [8] EP        SC4       BC2       TC_CD4    SC5       EC2       BC1      
#> [15] SC3       MC2       GC        SC6       MC1       TC_CD8   
#> 20 Levels: BC1 BC2 BC3 EC1 EC2 EP GC MC1 MC2 MC3 SC1 SC2 SC3 SC4 SC5 ... Undefined

# Set up cell populations
tumour = c("SC1", "SC2", "SC3", "SC4", "SC5", "SC6", "SC7")

bcells = c("BC1", "BC2", "BC3")
tcells = c("TC_CD4", "TC_CD8")
myeloid = c("MC1", "MC2", "MC3")

endothelial = c("EC1", "EC2")
epithelial = c("EP")

tissue = c(endothelial, epithelial)
immune = c(bcells, tcells, myeloid, "GC") #GC = granulocytes

all = c(tumour, tissue, immune, "Undefined")

4 Konditional

Konditional accepts a SingleCellExperiment object, or a single image and list of images from a SingleCellExperiment object, this gets passed into the imageData argument. The two cell types which will be evaluated are specified in the to and from arguments. A \(3^{rd}\) references population must also be specified in the parent argument, note the \(3^{rd}\) cell population must include the to cell type. The argument r will specify the radius which the cell relationship will be evaluated on. Konditional supports parallel processing, the number of cores can be specified using the cores argument. Konditional can take a single value or multiple values for each argument and will test all combinations of the arguments specified.

Here we test the relationship between CD4 T cells (TC_CD4) and one type of Tumour cell (SC5) with all immune cells being our reference population. The output is a data frame with the original L-function values and konditional values as well as the values for the arguments specified.

CD4_Konditional = Konditional(
    imageData = headSCE,
    r = 50,
    from = "TC_CD4",
    to = "SC5",
    parent = immune,
    cores = 40
)

CD4_Konditional
#>    imageID          test   original konditional  r weightQuantile inhom  edge
#> 1        1 TC_CD4 __ SC5 -11.504595 -13.4719284 50            0.8  TRUE FALSE
#> 2       12 TC_CD4 __ SC5 -24.778403 -12.1091628 50            0.8  TRUE FALSE
#> 3       13 TC_CD4 __ SC5 -13.971613 -10.1442932 50            0.8  TRUE FALSE
#> 4       14 TC_CD4 __ SC5 -17.882760 -22.0461047 50            0.8  TRUE FALSE
#> 5       15 TC_CD4 __ SC5  -1.849730   3.8472904 50            0.8  TRUE FALSE
#> 6       16 TC_CD4 __ SC5  -7.733687   4.0133489 50            0.8  TRUE FALSE
#> 7       17 TC_CD4 __ SC5   6.998017  11.3460420 50            0.8  TRUE FALSE
#> 8       18 TC_CD4 __ SC5   4.219412  -1.0138218 50            0.8  TRUE FALSE
#> 9       19 TC_CD4 __ SC5 -10.885027  -3.6913839 50            0.8  TRUE FALSE
#> 10      22 TC_CD4 __ SC5 -19.183807   4.4533957 50            0.8  TRUE FALSE
#> 11      23 TC_CD4 __ SC5  -7.753904  -0.5204235 50            0.8  TRUE FALSE
#> 12      24 TC_CD4 __ SC5  -5.944715  -7.1522676 50            0.8  TRUE FALSE
#> 13      25 TC_CD4 __ SC5  -6.943953  -7.2342587 50            0.8  TRUE FALSE
#> 14      26 TC_CD4 __ SC5 -10.888053  12.0075440 50            0.8  TRUE FALSE
#> 15      27 TC_CD4 __ SC5 -10.747546  -9.9940957 50            0.8  TRUE FALSE
#> 16      28 TC_CD4 __ SC5  -5.315542   3.3678342 50            0.8  TRUE FALSE
#> 17      29 TC_CD4 __ SC5  -5.041334   2.7358931 50            0.8  TRUE FALSE
#> 18      33 TC_CD4 __ SC5  -2.317716  -2.9852981 50            0.8  TRUE FALSE
#> 19      34 TC_CD4 __ SC5  -2.733872  -3.5834188 50            0.8  TRUE FALSE
#> 20      35 TC_CD4 __ SC5 -13.872572  -6.4535617 50            0.8  TRUE FALSE
#> 21      36 TC_CD4 __ SC5 -28.831695 -23.0128512 50            0.8  TRUE FALSE
#> 22      37 TC_CD4 __ SC5 -10.089565 -11.3751679 50            0.8  TRUE FALSE
#> 23      40 TC_CD4 __ SC5 -23.564587 -16.9603244 50            0.8  TRUE FALSE
#> 24      45 TC_CD4 __ SC5  -9.518718  -9.1885524 50            0.8  TRUE FALSE
#> 25      46 TC_CD4 __ SC5 -20.420499 -13.2796812 50            0.8  TRUE FALSE
#> 26       5 TC_CD4 __ SC5 -14.520368  -3.5710293 50            0.8  TRUE FALSE
#> 27       6 TC_CD4 __ SC5 -16.077982  -6.6252859 50            0.8  TRUE FALSE
#> 28       7 TC_CD4 __ SC5 -16.847385 -13.9845062 50            0.8  TRUE FALSE
#> 29       8 TC_CD4 __ SC5 -16.053892  -9.1938523 50            0.8  TRUE FALSE
#>    includeZeroCells window window.length
#> 1              TRUE convex            NA
#> 2              TRUE convex            NA
#> 3              TRUE convex            NA
#> 4              TRUE convex            NA
#> 5              TRUE convex            NA
#> 6              TRUE convex            NA
#> 7              TRUE convex            NA
#> 8              TRUE convex            NA
#> 9              TRUE convex            NA
#> 10             TRUE convex            NA
#> 11             TRUE convex            NA
#> 12             TRUE convex            NA
#> 13             TRUE convex            NA
#> 14             TRUE convex            NA
#> 15             TRUE convex            NA
#> 16             TRUE convex            NA
#> 17             TRUE convex            NA
#> 18             TRUE convex            NA
#> 19             TRUE convex            NA
#> 20             TRUE convex            NA
#> 21             TRUE convex            NA
#> 22             TRUE convex            NA
#> 23             TRUE convex            NA
#> 24             TRUE convex            NA
#> 25             TRUE convex            NA
#> 26             TRUE convex            NA
#> 27             TRUE convex            NA
#> 28             TRUE convex            NA
#> 29             TRUE convex            NA

The original and konditional values can be compared in a scatter plot to identify relationships which have been identified differently between the functions The top left quadrant represents values where Konditional has identified localisation between CD8 and SC5 and the original L-function has identified dispersion, the opposite is true for the bottom right quadrant.

plot = ggplot(CD4_Konditional, aes(x = original, y = konditional, col = imageID)) + 
    geom_point() +
    geom_hline(yintercept = 0, col = "red", linetype = "dashed") +
    geom_vline(xintercept = 0, col = "red", linetype = "dashed")

ggplotly(plot)
#> Warning: `gather_()` was deprecated in tidyr 1.2.0.
#> Please use `gather()` instead.

Alternatively all pairwise cell relationships and their corresponding parent in the dataset can be tested. A data frame with all pairwise combinations can be creating using the parentCombinations function. This function takes in a vector of all the cells, as well as all the parent vectors set up earlier. As shown below the output is a data frame specifying the to, from, and parent arguments for Kondtional.

# Get all relationships between cell types and their parents
parentDf = parentCombinations(all = all, tumour, bcells, tcells, myeloid, endothelial, epithelial, tissue, immune)
parentDf
#>       from        to       parent parent_name
#> 1      BC1       SC1 BC1, BC2....      bcells
#> 2      BC1       SC2 BC1, BC2....      bcells
#> 3      BC1       SC3 BC1, BC2....      bcells
#> 4      BC1       SC4 BC1, BC2....      bcells
#> 5      BC1       SC5 BC1, BC2....      bcells
#> 6      BC1       SC6 BC1, BC2....      bcells
#> 7      BC1       SC7 BC1, BC2....      bcells
#> 8      BC1       EC1 BC1, BC2....      bcells
#> 9      BC1       EC2 BC1, BC2....      bcells
#> 10     BC1        EP BC1, BC2....      bcells
#> 11     BC1       BC2 BC1, BC2....      bcells
#> 12     BC1       BC3 BC1, BC2....      bcells
#> 13     BC1    TC_CD4 BC1, BC2....      bcells
#> 14     BC1    TC_CD8 BC1, BC2....      bcells
#> 15     BC1       MC1 BC1, BC2....      bcells
#> 16     BC1       MC2 BC1, BC2....      bcells
#> 17     BC1       MC3 BC1, BC2....      bcells
#> 18     BC1        GC BC1, BC2....      bcells
#> 19     BC1 Undefined BC1, BC2....      bcells
#> 20     BC2       SC1 BC1, BC2....      bcells
#> 21     BC2       SC2 BC1, BC2....      bcells
#> 22     BC2       SC3 BC1, BC2....      bcells
#> 23     BC2       SC4 BC1, BC2....      bcells
#> 24     BC2       SC5 BC1, BC2....      bcells
#> 25     BC2       SC6 BC1, BC2....      bcells
#> 26     BC2       SC7 BC1, BC2....      bcells
#> 27     BC2       EC1 BC1, BC2....      bcells
#> 28     BC2       EC2 BC1, BC2....      bcells
#> 29     BC2        EP BC1, BC2....      bcells
#> 30     BC2       BC1 BC1, BC2....      bcells
#> 31     BC2       BC3 BC1, BC2....      bcells
#> 32     BC2    TC_CD4 BC1, BC2....      bcells
#> 33     BC2    TC_CD8 BC1, BC2....      bcells
#> 34     BC2       MC1 BC1, BC2....      bcells
#> 35     BC2       MC2 BC1, BC2....      bcells
#> 36     BC2       MC3 BC1, BC2....      bcells
#> 37     BC2        GC BC1, BC2....      bcells
#> 38     BC2 Undefined BC1, BC2....      bcells
#> 39     BC3       SC1 BC1, BC2....      bcells
#> 40     BC3       SC2 BC1, BC2....      bcells
#> 41     BC3       SC3 BC1, BC2....      bcells
#> 42     BC3       SC4 BC1, BC2....      bcells
#> 43     BC3       SC5 BC1, BC2....      bcells
#> 44     BC3       SC6 BC1, BC2....      bcells
#> 45     BC3       SC7 BC1, BC2....      bcells
#> 46     BC3       EC1 BC1, BC2....      bcells
#> 47     BC3       EC2 BC1, BC2....      bcells
#> 48     BC3        EP BC1, BC2....      bcells
#> 49     BC3       BC1 BC1, BC2....      bcells
#> 50     BC3       BC2 BC1, BC2....      bcells
#> 51     BC3    TC_CD4 BC1, BC2....      bcells
#> 52     BC3    TC_CD8 BC1, BC2....      bcells
#> 53     BC3       MC1 BC1, BC2....      bcells
#> 54     BC3       MC2 BC1, BC2....      bcells
#> 55     BC3       MC3 BC1, BC2....      bcells
#> 56     BC3        GC BC1, BC2....      bcells
#> 57     BC3 Undefined BC1, BC2....      bcells
#> 58     EC1       SC1     EC1, EC2 endothelial
#> 59     EC1       SC2     EC1, EC2 endothelial
#> 60     EC1       SC3     EC1, EC2 endothelial
#> 61     EC1       SC4     EC1, EC2 endothelial
#> 62     EC1       SC5     EC1, EC2 endothelial
#> 63     EC1       SC6     EC1, EC2 endothelial
#> 64     EC1       SC7     EC1, EC2 endothelial
#> 65     EC1       EC2     EC1, EC2 endothelial
#> 66     EC1        EP     EC1, EC2 endothelial
#> 67     EC1       BC1     EC1, EC2 endothelial
#> 68     EC1       BC2     EC1, EC2 endothelial
#> 69     EC1       BC3     EC1, EC2 endothelial
#> 70     EC1    TC_CD4     EC1, EC2 endothelial
#> 71     EC1    TC_CD8     EC1, EC2 endothelial
#> 72     EC1       MC1     EC1, EC2 endothelial
#> 73     EC1       MC2     EC1, EC2 endothelial
#> 74     EC1       MC3     EC1, EC2 endothelial
#> 75     EC1        GC     EC1, EC2 endothelial
#> 76     EC1 Undefined     EC1, EC2 endothelial
#> 77     EC2       SC1     EC1, EC2 endothelial
#> 78     EC2       SC2     EC1, EC2 endothelial
#> 79     EC2       SC3     EC1, EC2 endothelial
#> 80     EC2       SC4     EC1, EC2 endothelial
#> 81     EC2       SC5     EC1, EC2 endothelial
#> 82     EC2       SC6     EC1, EC2 endothelial
#> 83     EC2       SC7     EC1, EC2 endothelial
#> 84     EC2       EC1     EC1, EC2 endothelial
#> 85     EC2        EP     EC1, EC2 endothelial
#> 86     EC2       BC1     EC1, EC2 endothelial
#> 87     EC2       BC2     EC1, EC2 endothelial
#> 88     EC2       BC3     EC1, EC2 endothelial
#> 89     EC2    TC_CD4     EC1, EC2 endothelial
#> 90     EC2    TC_CD8     EC1, EC2 endothelial
#> 91     EC2       MC1     EC1, EC2 endothelial
#> 92     EC2       MC2     EC1, EC2 endothelial
#> 93     EC2       MC3     EC1, EC2 endothelial
#> 94     EC2        GC     EC1, EC2 endothelial
#> 95     EC2 Undefined     EC1, EC2 endothelial
#> 96      EP       SC1           EP  epithelial
#> 97      EP       SC2           EP  epithelial
#> 98      EP       SC3           EP  epithelial
#> 99      EP       SC4           EP  epithelial
#> 100     EP       SC5           EP  epithelial
#> 101     EP       SC6           EP  epithelial
#> 102     EP       SC7           EP  epithelial
#> 103     EP       EC1           EP  epithelial
#> 104     EP       EC2           EP  epithelial
#> 105     EP       BC1           EP  epithelial
#> 106     EP       BC2           EP  epithelial
#> 107     EP       BC3           EP  epithelial
#> 108     EP    TC_CD4           EP  epithelial
#> 109     EP    TC_CD8           EP  epithelial
#> 110     EP       MC1           EP  epithelial
#> 111     EP       MC2           EP  epithelial
#> 112     EP       MC3           EP  epithelial
#> 113     EP        GC           EP  epithelial
#> 114     EP Undefined           EP  epithelial
#> 115    BC1       SC1 BC1, BC2....      immune
#> 116    BC1       SC2 BC1, BC2....      immune
#> 117    BC1       SC3 BC1, BC2....      immune
#> 118    BC1       SC4 BC1, BC2....      immune
#> 119    BC1       SC5 BC1, BC2....      immune
#> 120    BC1       SC6 BC1, BC2....      immune
#> 121    BC1       SC7 BC1, BC2....      immune
#> 122    BC1       EC1 BC1, BC2....      immune
#> 123    BC1       EC2 BC1, BC2....      immune
#> 124    BC1        EP BC1, BC2....      immune
#> 125    BC1       BC2 BC1, BC2....      immune
#> 126    BC1       BC3 BC1, BC2....      immune
#> 127    BC1    TC_CD4 BC1, BC2....      immune
#> 128    BC1    TC_CD8 BC1, BC2....      immune
#> 129    BC1       MC1 BC1, BC2....      immune
#> 130    BC1       MC2 BC1, BC2....      immune
#> 131    BC1       MC3 BC1, BC2....      immune
#> 132    BC1        GC BC1, BC2....      immune
#> 133    BC1 Undefined BC1, BC2....      immune
#> 134    BC2       SC1 BC1, BC2....      immune
#> 135    BC2       SC2 BC1, BC2....      immune
#> 136    BC2       SC3 BC1, BC2....      immune
#> 137    BC2       SC4 BC1, BC2....      immune
#> 138    BC2       SC5 BC1, BC2....      immune
#> 139    BC2       SC6 BC1, BC2....      immune
#> 140    BC2       SC7 BC1, BC2....      immune
#> 141    BC2       EC1 BC1, BC2....      immune
#> 142    BC2       EC2 BC1, BC2....      immune
#> 143    BC2        EP BC1, BC2....      immune
#> 144    BC2       BC1 BC1, BC2....      immune
#> 145    BC2       BC3 BC1, BC2....      immune
#> 146    BC2    TC_CD4 BC1, BC2....      immune
#> 147    BC2    TC_CD8 BC1, BC2....      immune
#> 148    BC2       MC1 BC1, BC2....      immune
#> 149    BC2       MC2 BC1, BC2....      immune
#> 150    BC2       MC3 BC1, BC2....      immune
#> 151    BC2        GC BC1, BC2....      immune
#> 152    BC2 Undefined BC1, BC2....      immune
#> 153    BC3       SC1 BC1, BC2....      immune
#> 154    BC3       SC2 BC1, BC2....      immune
#> 155    BC3       SC3 BC1, BC2....      immune
#> 156    BC3       SC4 BC1, BC2....      immune
#> 157    BC3       SC5 BC1, BC2....      immune
#> 158    BC3       SC6 BC1, BC2....      immune
#> 159    BC3       SC7 BC1, BC2....      immune
#> 160    BC3       EC1 BC1, BC2....      immune
#> 161    BC3       EC2 BC1, BC2....      immune
#> 162    BC3        EP BC1, BC2....      immune
#> 163    BC3       BC1 BC1, BC2....      immune
#> 164    BC3       BC2 BC1, BC2....      immune
#> 165    BC3    TC_CD4 BC1, BC2....      immune
#> 166    BC3    TC_CD8 BC1, BC2....      immune
#> 167    BC3       MC1 BC1, BC2....      immune
#> 168    BC3       MC2 BC1, BC2....      immune
#> 169    BC3       MC3 BC1, BC2....      immune
#> 170    BC3        GC BC1, BC2....      immune
#> 171    BC3 Undefined BC1, BC2....      immune
#> 172     GC       SC1 BC1, BC2....      immune
#> 173     GC       SC2 BC1, BC2....      immune
#> 174     GC       SC3 BC1, BC2....      immune
#> 175     GC       SC4 BC1, BC2....      immune
#> 176     GC       SC5 BC1, BC2....      immune
#> 177     GC       SC6 BC1, BC2....      immune
#> 178     GC       SC7 BC1, BC2....      immune
#> 179     GC       EC1 BC1, BC2....      immune
#> 180     GC       EC2 BC1, BC2....      immune
#> 181     GC        EP BC1, BC2....      immune
#> 182     GC       BC1 BC1, BC2....      immune
#> 183     GC       BC2 BC1, BC2....      immune
#> 184     GC       BC3 BC1, BC2....      immune
#> 185     GC    TC_CD4 BC1, BC2....      immune
#> 186     GC    TC_CD8 BC1, BC2....      immune
#> 187     GC       MC1 BC1, BC2....      immune
#> 188     GC       MC2 BC1, BC2....      immune
#> 189     GC       MC3 BC1, BC2....      immune
#> 190     GC Undefined BC1, BC2....      immune
#> 191    MC1       SC1 BC1, BC2....      immune
#> 192    MC1       SC2 BC1, BC2....      immune
#> 193    MC1       SC3 BC1, BC2....      immune
#> 194    MC1       SC4 BC1, BC2....      immune
#> 195    MC1       SC5 BC1, BC2....      immune
#> 196    MC1       SC6 BC1, BC2....      immune
#> 197    MC1       SC7 BC1, BC2....      immune
#> 198    MC1       EC1 BC1, BC2....      immune
#> 199    MC1       EC2 BC1, BC2....      immune
#> 200    MC1        EP BC1, BC2....      immune
#> 201    MC1       BC1 BC1, BC2....      immune
#> 202    MC1       BC2 BC1, BC2....      immune
#> 203    MC1       BC3 BC1, BC2....      immune
#> 204    MC1    TC_CD4 BC1, BC2....      immune
#> 205    MC1    TC_CD8 BC1, BC2....      immune
#> 206    MC1       MC2 BC1, BC2....      immune
#> 207    MC1       MC3 BC1, BC2....      immune
#> 208    MC1        GC BC1, BC2....      immune
#> 209    MC1 Undefined BC1, BC2....      immune
#> 210    MC2       SC1 BC1, BC2....      immune
#> 211    MC2       SC2 BC1, BC2....      immune
#> 212    MC2       SC3 BC1, BC2....      immune
#> 213    MC2       SC4 BC1, BC2....      immune
#> 214    MC2       SC5 BC1, BC2....      immune
#> 215    MC2       SC6 BC1, BC2....      immune
#> 216    MC2       SC7 BC1, BC2....      immune
#> 217    MC2       EC1 BC1, BC2....      immune
#> 218    MC2       EC2 BC1, BC2....      immune
#> 219    MC2        EP BC1, BC2....      immune
#> 220    MC2       BC1 BC1, BC2....      immune
#> 221    MC2       BC2 BC1, BC2....      immune
#> 222    MC2       BC3 BC1, BC2....      immune
#> 223    MC2    TC_CD4 BC1, BC2....      immune
#> 224    MC2    TC_CD8 BC1, BC2....      immune
#> 225    MC2       MC1 BC1, BC2....      immune
#> 226    MC2       MC3 BC1, BC2....      immune
#> 227    MC2        GC BC1, BC2....      immune
#> 228    MC2 Undefined BC1, BC2....      immune
#> 229    MC3       SC1 BC1, BC2....      immune
#> 230    MC3       SC2 BC1, BC2....      immune
#> 231    MC3       SC3 BC1, BC2....      immune
#> 232    MC3       SC4 BC1, BC2....      immune
#> 233    MC3       SC5 BC1, BC2....      immune
#> 234    MC3       SC6 BC1, BC2....      immune
#> 235    MC3       SC7 BC1, BC2....      immune
#> 236    MC3       EC1 BC1, BC2....      immune
#> 237    MC3       EC2 BC1, BC2....      immune
#> 238    MC3        EP BC1, BC2....      immune
#> 239    MC3       BC1 BC1, BC2....      immune
#> 240    MC3       BC2 BC1, BC2....      immune
#> 241    MC3       BC3 BC1, BC2....      immune
#> 242    MC3    TC_CD4 BC1, BC2....      immune
#> 243    MC3    TC_CD8 BC1, BC2....      immune
#> 244    MC3       MC1 BC1, BC2....      immune
#> 245    MC3       MC2 BC1, BC2....      immune
#> 246    MC3        GC BC1, BC2....      immune
#> 247    MC3 Undefined BC1, BC2....      immune
#> 248 TC_CD4       SC1 BC1, BC2....      immune
#> 249 TC_CD4       SC2 BC1, BC2....      immune
#> 250 TC_CD4       SC3 BC1, BC2....      immune
#> 251 TC_CD4       SC4 BC1, BC2....      immune
#> 252 TC_CD4       SC5 BC1, BC2....      immune
#> 253 TC_CD4       SC6 BC1, BC2....      immune
#> 254 TC_CD4       SC7 BC1, BC2....      immune
#> 255 TC_CD4       EC1 BC1, BC2....      immune
#> 256 TC_CD4       EC2 BC1, BC2....      immune
#> 257 TC_CD4        EP BC1, BC2....      immune
#> 258 TC_CD4       BC1 BC1, BC2....      immune
#> 259 TC_CD4       BC2 BC1, BC2....      immune
#> 260 TC_CD4       BC3 BC1, BC2....      immune
#> 261 TC_CD4    TC_CD8 BC1, BC2....      immune
#> 262 TC_CD4       MC1 BC1, BC2....      immune
#> 263 TC_CD4       MC2 BC1, BC2....      immune
#> 264 TC_CD4       MC3 BC1, BC2....      immune
#> 265 TC_CD4        GC BC1, BC2....      immune
#> 266 TC_CD4 Undefined BC1, BC2....      immune
#> 267 TC_CD8       SC1 BC1, BC2....      immune
#> 268 TC_CD8       SC2 BC1, BC2....      immune
#> 269 TC_CD8       SC3 BC1, BC2....      immune
#> 270 TC_CD8       SC4 BC1, BC2....      immune
#> 271 TC_CD8       SC5 BC1, BC2....      immune
#> 272 TC_CD8       SC6 BC1, BC2....      immune
#> 273 TC_CD8       SC7 BC1, BC2....      immune
#> 274 TC_CD8       EC1 BC1, BC2....      immune
#> 275 TC_CD8       EC2 BC1, BC2....      immune
#> 276 TC_CD8        EP BC1, BC2....      immune
#> 277 TC_CD8       BC1 BC1, BC2....      immune
#> 278 TC_CD8       BC2 BC1, BC2....      immune
#> 279 TC_CD8       BC3 BC1, BC2....      immune
#> 280 TC_CD8    TC_CD4 BC1, BC2....      immune
#> 281 TC_CD8       MC1 BC1, BC2....      immune
#> 282 TC_CD8       MC2 BC1, BC2....      immune
#> 283 TC_CD8       MC3 BC1, BC2....      immune
#> 284 TC_CD8        GC BC1, BC2....      immune
#> 285 TC_CD8 Undefined BC1, BC2....      immune
#> 286    MC1       SC1 MC1, MC2....     myeloid
#> 287    MC1       SC2 MC1, MC2....     myeloid
#> 288    MC1       SC3 MC1, MC2....     myeloid
#> 289    MC1       SC4 MC1, MC2....     myeloid
#> 290    MC1       SC5 MC1, MC2....     myeloid
#> 291    MC1       SC6 MC1, MC2....     myeloid
#> 292    MC1       SC7 MC1, MC2....     myeloid
#> 293    MC1       EC1 MC1, MC2....     myeloid
#> 294    MC1       EC2 MC1, MC2....     myeloid
#> 295    MC1        EP MC1, MC2....     myeloid
#> 296    MC1       BC1 MC1, MC2....     myeloid
#> 297    MC1       BC2 MC1, MC2....     myeloid
#> 298    MC1       BC3 MC1, MC2....     myeloid
#> 299    MC1    TC_CD4 MC1, MC2....     myeloid
#> 300    MC1    TC_CD8 MC1, MC2....     myeloid
#> 301    MC1       MC2 MC1, MC2....     myeloid
#> 302    MC1       MC3 MC1, MC2....     myeloid
#> 303    MC1        GC MC1, MC2....     myeloid
#> 304    MC1 Undefined MC1, MC2....     myeloid
#> 305    MC2       SC1 MC1, MC2....     myeloid
#> 306    MC2       SC2 MC1, MC2....     myeloid
#> 307    MC2       SC3 MC1, MC2....     myeloid
#> 308    MC2       SC4 MC1, MC2....     myeloid
#> 309    MC2       SC5 MC1, MC2....     myeloid
#> 310    MC2       SC6 MC1, MC2....     myeloid
#> 311    MC2       SC7 MC1, MC2....     myeloid
#> 312    MC2       EC1 MC1, MC2....     myeloid
#> 313    MC2       EC2 MC1, MC2....     myeloid
#> 314    MC2        EP MC1, MC2....     myeloid
#> 315    MC2       BC1 MC1, MC2....     myeloid
#> 316    MC2       BC2 MC1, MC2....     myeloid
#> 317    MC2       BC3 MC1, MC2....     myeloid
#> 318    MC2    TC_CD4 MC1, MC2....     myeloid
#> 319    MC2    TC_CD8 MC1, MC2....     myeloid
#> 320    MC2       MC1 MC1, MC2....     myeloid
#> 321    MC2       MC3 MC1, MC2....     myeloid
#> 322    MC2        GC MC1, MC2....     myeloid
#> 323    MC2 Undefined MC1, MC2....     myeloid
#> 324    MC3       SC1 MC1, MC2....     myeloid
#> 325    MC3       SC2 MC1, MC2....     myeloid
#> 326    MC3       SC3 MC1, MC2....     myeloid
#> 327    MC3       SC4 MC1, MC2....     myeloid
#> 328    MC3       SC5 MC1, MC2....     myeloid
#> 329    MC3       SC6 MC1, MC2....     myeloid
#> 330    MC3       SC7 MC1, MC2....     myeloid
#> 331    MC3       EC1 MC1, MC2....     myeloid
#> 332    MC3       EC2 MC1, MC2....     myeloid
#> 333    MC3        EP MC1, MC2....     myeloid
#> 334    MC3       BC1 MC1, MC2....     myeloid
#> 335    MC3       BC2 MC1, MC2....     myeloid
#> 336    MC3       BC3 MC1, MC2....     myeloid
#> 337    MC3    TC_CD4 MC1, MC2....     myeloid
#> 338    MC3    TC_CD8 MC1, MC2....     myeloid
#> 339    MC3       MC1 MC1, MC2....     myeloid
#> 340    MC3       MC2 MC1, MC2....     myeloid
#> 341    MC3        GC MC1, MC2....     myeloid
#> 342    MC3 Undefined MC1, MC2....     myeloid
#> 343 TC_CD4       SC1 TC_CD4, ....      tcells
#> 344 TC_CD4       SC2 TC_CD4, ....      tcells
#> 345 TC_CD4       SC3 TC_CD4, ....      tcells
#> 346 TC_CD4       SC4 TC_CD4, ....      tcells
#> 347 TC_CD4       SC5 TC_CD4, ....      tcells
#> 348 TC_CD4       SC6 TC_CD4, ....      tcells
#> 349 TC_CD4       SC7 TC_CD4, ....      tcells
#> 350 TC_CD4       EC1 TC_CD4, ....      tcells
#> 351 TC_CD4       EC2 TC_CD4, ....      tcells
#> 352 TC_CD4        EP TC_CD4, ....      tcells
#> 353 TC_CD4       BC1 TC_CD4, ....      tcells
#> 354 TC_CD4       BC2 TC_CD4, ....      tcells
#> 355 TC_CD4       BC3 TC_CD4, ....      tcells
#> 356 TC_CD4    TC_CD8 TC_CD4, ....      tcells
#> 357 TC_CD4       MC1 TC_CD4, ....      tcells
#> 358 TC_CD4       MC2 TC_CD4, ....      tcells
#> 359 TC_CD4       MC3 TC_CD4, ....      tcells
#> 360 TC_CD4        GC TC_CD4, ....      tcells
#> 361 TC_CD4 Undefined TC_CD4, ....      tcells
#> 362 TC_CD8       SC1 TC_CD4, ....      tcells
#> 363 TC_CD8       SC2 TC_CD4, ....      tcells
#> 364 TC_CD8       SC3 TC_CD4, ....      tcells
#> 365 TC_CD8       SC4 TC_CD4, ....      tcells
#> 366 TC_CD8       SC5 TC_CD4, ....      tcells
#> 367 TC_CD8       SC6 TC_CD4, ....      tcells
#> 368 TC_CD8       SC7 TC_CD4, ....      tcells
#> 369 TC_CD8       EC1 TC_CD4, ....      tcells
#> 370 TC_CD8       EC2 TC_CD4, ....      tcells
#> 371 TC_CD8        EP TC_CD4, ....      tcells
#> 372 TC_CD8       BC1 TC_CD4, ....      tcells
#> 373 TC_CD8       BC2 TC_CD4, ....      tcells
#> 374 TC_CD8       BC3 TC_CD4, ....      tcells
#> 375 TC_CD8    TC_CD4 TC_CD4, ....      tcells
#> 376 TC_CD8       MC1 TC_CD4, ....      tcells
#> 377 TC_CD8       MC2 TC_CD4, ....      tcells
#> 378 TC_CD8       MC3 TC_CD4, ....      tcells
#> 379 TC_CD8        GC TC_CD4, ....      tcells
#> 380 TC_CD8 Undefined TC_CD4, ....      tcells
#> 381    EC1       SC1 EC1, EC2, EP      tissue
#> 382    EC1       SC2 EC1, EC2, EP      tissue
#> 383    EC1       SC3 EC1, EC2, EP      tissue
#> 384    EC1       SC4 EC1, EC2, EP      tissue
#> 385    EC1       SC5 EC1, EC2, EP      tissue
#> 386    EC1       SC6 EC1, EC2, EP      tissue
#> 387    EC1       SC7 EC1, EC2, EP      tissue
#> 388    EC1       EC2 EC1, EC2, EP      tissue
#> 389    EC1        EP EC1, EC2, EP      tissue
#> 390    EC1       BC1 EC1, EC2, EP      tissue
#> 391    EC1       BC2 EC1, EC2, EP      tissue
#> 392    EC1       BC3 EC1, EC2, EP      tissue
#> 393    EC1    TC_CD4 EC1, EC2, EP      tissue
#> 394    EC1    TC_CD8 EC1, EC2, EP      tissue
#> 395    EC1       MC1 EC1, EC2, EP      tissue
#> 396    EC1       MC2 EC1, EC2, EP      tissue
#> 397    EC1       MC3 EC1, EC2, EP      tissue
#> 398    EC1        GC EC1, EC2, EP      tissue
#> 399    EC1 Undefined EC1, EC2, EP      tissue
#> 400    EC2       SC1 EC1, EC2, EP      tissue
#> 401    EC2       SC2 EC1, EC2, EP      tissue
#> 402    EC2       SC3 EC1, EC2, EP      tissue
#> 403    EC2       SC4 EC1, EC2, EP      tissue
#> 404    EC2       SC5 EC1, EC2, EP      tissue
#> 405    EC2       SC6 EC1, EC2, EP      tissue
#> 406    EC2       SC7 EC1, EC2, EP      tissue
#> 407    EC2       EC1 EC1, EC2, EP      tissue
#> 408    EC2        EP EC1, EC2, EP      tissue
#> 409    EC2       BC1 EC1, EC2, EP      tissue
#> 410    EC2       BC2 EC1, EC2, EP      tissue
#> 411    EC2       BC3 EC1, EC2, EP      tissue
#> 412    EC2    TC_CD4 EC1, EC2, EP      tissue
#> 413    EC2    TC_CD8 EC1, EC2, EP      tissue
#> 414    EC2       MC1 EC1, EC2, EP      tissue
#> 415    EC2       MC2 EC1, EC2, EP      tissue
#> 416    EC2       MC3 EC1, EC2, EP      tissue
#> 417    EC2        GC EC1, EC2, EP      tissue
#> 418    EC2 Undefined EC1, EC2, EP      tissue
#> 419     EP       SC1 EC1, EC2, EP      tissue
#> 420     EP       SC2 EC1, EC2, EP      tissue
#> 421     EP       SC3 EC1, EC2, EP      tissue
#> 422     EP       SC4 EC1, EC2, EP      tissue
#> 423     EP       SC5 EC1, EC2, EP      tissue
#> 424     EP       SC6 EC1, EC2, EP      tissue
#> 425     EP       SC7 EC1, EC2, EP      tissue
#> 426     EP       EC1 EC1, EC2, EP      tissue
#> 427     EP       EC2 EC1, EC2, EP      tissue
#> 428     EP       BC1 EC1, EC2, EP      tissue
#> 429     EP       BC2 EC1, EC2, EP      tissue
#> 430     EP       BC3 EC1, EC2, EP      tissue
#> 431     EP    TC_CD4 EC1, EC2, EP      tissue
#> 432     EP    TC_CD8 EC1, EC2, EP      tissue
#> 433     EP       MC1 EC1, EC2, EP      tissue
#> 434     EP       MC2 EC1, EC2, EP      tissue
#> 435     EP       MC3 EC1, EC2, EP      tissue
#> 436     EP        GC EC1, EC2, EP      tissue
#> 437     EP Undefined EC1, EC2, EP      tissue
#> 438    SC1       SC2 SC1, SC2....      tumour
#> 439    SC1       SC3 SC1, SC2....      tumour
#> 440    SC1       SC4 SC1, SC2....      tumour
#> 441    SC1       SC5 SC1, SC2....      tumour
#> 442    SC1       SC6 SC1, SC2....      tumour
#> 443    SC1       SC7 SC1, SC2....      tumour
#> 444    SC1       EC1 SC1, SC2....      tumour
#> 445    SC1       EC2 SC1, SC2....      tumour
#> 446    SC1        EP SC1, SC2....      tumour
#> 447    SC1       BC1 SC1, SC2....      tumour
#> 448    SC1       BC2 SC1, SC2....      tumour
#> 449    SC1       BC3 SC1, SC2....      tumour
#> 450    SC1    TC_CD4 SC1, SC2....      tumour
#> 451    SC1    TC_CD8 SC1, SC2....      tumour
#> 452    SC1       MC1 SC1, SC2....      tumour
#> 453    SC1       MC2 SC1, SC2....      tumour
#> 454    SC1       MC3 SC1, SC2....      tumour
#> 455    SC1        GC SC1, SC2....      tumour
#> 456    SC1 Undefined SC1, SC2....      tumour
#> 457    SC2       SC1 SC1, SC2....      tumour
#> 458    SC2       SC3 SC1, SC2....      tumour
#> 459    SC2       SC4 SC1, SC2....      tumour
#> 460    SC2       SC5 SC1, SC2....      tumour
#> 461    SC2       SC6 SC1, SC2....      tumour
#> 462    SC2       SC7 SC1, SC2....      tumour
#> 463    SC2       EC1 SC1, SC2....      tumour
#> 464    SC2       EC2 SC1, SC2....      tumour
#> 465    SC2        EP SC1, SC2....      tumour
#> 466    SC2       BC1 SC1, SC2....      tumour
#> 467    SC2       BC2 SC1, SC2....      tumour
#> 468    SC2       BC3 SC1, SC2....      tumour
#> 469    SC2    TC_CD4 SC1, SC2....      tumour
#> 470    SC2    TC_CD8 SC1, SC2....      tumour
#> 471    SC2       MC1 SC1, SC2....      tumour
#> 472    SC2       MC2 SC1, SC2....      tumour
#> 473    SC2       MC3 SC1, SC2....      tumour
#> 474    SC2        GC SC1, SC2....      tumour
#> 475    SC2 Undefined SC1, SC2....      tumour
#> 476    SC3       SC1 SC1, SC2....      tumour
#> 477    SC3       SC2 SC1, SC2....      tumour
#> 478    SC3       SC4 SC1, SC2....      tumour
#> 479    SC3       SC5 SC1, SC2....      tumour
#> 480    SC3       SC6 SC1, SC2....      tumour
#> 481    SC3       SC7 SC1, SC2....      tumour
#> 482    SC3       EC1 SC1, SC2....      tumour
#> 483    SC3       EC2 SC1, SC2....      tumour
#> 484    SC3        EP SC1, SC2....      tumour
#> 485    SC3       BC1 SC1, SC2....      tumour
#> 486    SC3       BC2 SC1, SC2....      tumour
#> 487    SC3       BC3 SC1, SC2....      tumour
#> 488    SC3    TC_CD4 SC1, SC2....      tumour
#> 489    SC3    TC_CD8 SC1, SC2....      tumour
#> 490    SC3       MC1 SC1, SC2....      tumour
#> 491    SC3       MC2 SC1, SC2....      tumour
#> 492    SC3       MC3 SC1, SC2....      tumour
#> 493    SC3        GC SC1, SC2....      tumour
#> 494    SC3 Undefined SC1, SC2....      tumour
#> 495    SC4       SC1 SC1, SC2....      tumour
#> 496    SC4       SC2 SC1, SC2....      tumour
#> 497    SC4       SC3 SC1, SC2....      tumour
#> 498    SC4       SC5 SC1, SC2....      tumour
#> 499    SC4       SC6 SC1, SC2....      tumour
#> 500    SC4       SC7 SC1, SC2....      tumour
#> 501    SC4       EC1 SC1, SC2....      tumour
#> 502    SC4       EC2 SC1, SC2....      tumour
#> 503    SC4        EP SC1, SC2....      tumour
#> 504    SC4       BC1 SC1, SC2....      tumour
#> 505    SC4       BC2 SC1, SC2....      tumour
#> 506    SC4       BC3 SC1, SC2....      tumour
#> 507    SC4    TC_CD4 SC1, SC2....      tumour
#> 508    SC4    TC_CD8 SC1, SC2....      tumour
#> 509    SC4       MC1 SC1, SC2....      tumour
#> 510    SC4       MC2 SC1, SC2....      tumour
#> 511    SC4       MC3 SC1, SC2....      tumour
#> 512    SC4        GC SC1, SC2....      tumour
#> 513    SC4 Undefined SC1, SC2....      tumour
#> 514    SC5       SC1 SC1, SC2....      tumour
#> 515    SC5       SC2 SC1, SC2....      tumour
#> 516    SC5       SC3 SC1, SC2....      tumour
#> 517    SC5       SC4 SC1, SC2....      tumour
#> 518    SC5       SC6 SC1, SC2....      tumour
#> 519    SC5       SC7 SC1, SC2....      tumour
#> 520    SC5       EC1 SC1, SC2....      tumour
#> 521    SC5       EC2 SC1, SC2....      tumour
#> 522    SC5        EP SC1, SC2....      tumour
#> 523    SC5       BC1 SC1, SC2....      tumour
#> 524    SC5       BC2 SC1, SC2....      tumour
#> 525    SC5       BC3 SC1, SC2....      tumour
#> 526    SC5    TC_CD4 SC1, SC2....      tumour
#> 527    SC5    TC_CD8 SC1, SC2....      tumour
#> 528    SC5       MC1 SC1, SC2....      tumour
#> 529    SC5       MC2 SC1, SC2....      tumour
#> 530    SC5       MC3 SC1, SC2....      tumour
#> 531    SC5        GC SC1, SC2....      tumour
#> 532    SC5 Undefined SC1, SC2....      tumour
#> 533    SC6       SC1 SC1, SC2....      tumour
#> 534    SC6       SC2 SC1, SC2....      tumour
#> 535    SC6       SC3 SC1, SC2....      tumour
#> 536    SC6       SC4 SC1, SC2....      tumour
#> 537    SC6       SC5 SC1, SC2....      tumour
#> 538    SC6       SC7 SC1, SC2....      tumour
#> 539    SC6       EC1 SC1, SC2....      tumour
#> 540    SC6       EC2 SC1, SC2....      tumour
#> 541    SC6        EP SC1, SC2....      tumour
#> 542    SC6       BC1 SC1, SC2....      tumour
#> 543    SC6       BC2 SC1, SC2....      tumour
#> 544    SC6       BC3 SC1, SC2....      tumour
#> 545    SC6    TC_CD4 SC1, SC2....      tumour
#> 546    SC6    TC_CD8 SC1, SC2....      tumour
#> 547    SC6       MC1 SC1, SC2....      tumour
#> 548    SC6       MC2 SC1, SC2....      tumour
#> 549    SC6       MC3 SC1, SC2....      tumour
#> 550    SC6        GC SC1, SC2....      tumour
#> 551    SC6 Undefined SC1, SC2....      tumour
#> 552    SC7       SC1 SC1, SC2....      tumour
#> 553    SC7       SC2 SC1, SC2....      tumour
#> 554    SC7       SC3 SC1, SC2....      tumour
#> 555    SC7       SC4 SC1, SC2....      tumour
#> 556    SC7       SC5 SC1, SC2....      tumour
#> 557    SC7       SC6 SC1, SC2....      tumour
#> 558    SC7       EC1 SC1, SC2....      tumour
#> 559    SC7       EC2 SC1, SC2....      tumour
#> 560    SC7        EP SC1, SC2....      tumour
#> 561    SC7       BC1 SC1, SC2....      tumour
#> 562    SC7       BC2 SC1, SC2....      tumour
#> 563    SC7       BC3 SC1, SC2....      tumour
#> 564    SC7    TC_CD4 SC1, SC2....      tumour
#> 565    SC7    TC_CD8 SC1, SC2....      tumour
#> 566    SC7       MC1 SC1, SC2....      tumour
#> 567    SC7       MC2 SC1, SC2....      tumour
#> 568    SC7       MC3 SC1, SC2....      tumour
#> 569    SC7        GC SC1, SC2....      tumour
#> 570    SC7 Undefined SC1, SC2....      tumour

Rather than specifying to, from, and parent in Konditional, the output from parentCombinations can be inputed into Konditional. Here we will test all pairwise cell relationships on the first image of the dataset.

# Selecting Image 1 as an example
image_1 = headSCE %>% colData %>% data.frame() %>% filter(imageID == "1")


image1_Konditional = Konditional(image_1, 
                                parentDf = parentDf,
                                r = 50,
                                cores = 40)
image1_Konditional
#>     imageID                            test     original  konditional  r
#> 1         1            BC1 __ SC1 __ bcells   0.76301875   4.63044955 50
#> 2         1            BC1 __ SC2 __ bcells  -7.47059261  -8.57124590 50
#> 3         1            BC1 __ SC3 __ bcells  -9.37793451 -10.46948640 50
#> 4         1            BC1 __ SC4 __ bcells   1.13997646  -1.81370492 50
#> 5         1            BC1 __ SC5 __ bcells   6.92458926   5.26339160 50
#> 6         1            BC1 __ SC6 __ bcells  -8.28486988  -4.65707551 50
#> 7         1            BC1 __ SC7 __ bcells  -7.13642931  -6.02868980 50
#> 8         1            BC1 __ EC1 __ bcells -24.57970886  -9.61217548 50
#> 9         1            BC1 __ EC2 __ bcells -14.12189347 -12.91058016 50
#> 10        1             BC1 __ EP __ bcells  -4.37129472  14.62754950 50
#> 11        1            BC1 __ BC2 __ bcells  -7.10583144  -5.02830294 50
#> 12        1            BC1 __ BC3 __ bcells   1.88827295  -3.19797575 50
#> 13        1         BC1 __ TC_CD4 __ bcells -17.88982667  -4.48718396 50
#> 14        1         BC1 __ TC_CD8 __ bcells  -6.91600512  -1.04530433 50
#> 15        1            BC1 __ MC1 __ bcells -21.11848451  -8.25057762 50
#> 16        1            BC1 __ MC2 __ bcells -13.70128934  -2.97572877 50
#> 17        1            BC1 __ MC3 __ bcells  -8.44703838  -2.85566810 50
#> 18        1             BC1 __ GC __ bcells -27.56957741 -18.80714781 50
#> 19        1      BC1 __ Undefined __ bcells  -4.64746577  -3.19472608 50
#> 20        1            BC2 __ SC1 __ bcells   1.82752333   5.85377833 50
#> 21        1            BC2 __ SC2 __ bcells   2.45879059   0.57434325 50
#> 22        1            BC2 __ SC3 __ bcells   1.35981727  -0.66632514 50
#> 23        1            BC2 __ SC4 __ bcells   1.05102750  -1.65106898 50
#> 24        1            BC2 __ SC5 __ bcells   0.43019776  -1.77528327 50
#> 25        1            BC2 __ SC6 __ bcells   3.64561767  10.36071570 50
#> 26        1            BC2 __ SC7 __ bcells   1.49766950   1.94770417 50
#> 27        1            BC2 __ EC1 __ bcells  -0.23030303  28.66843383 50
#> 28        1            BC2 __ EC2 __ bcells   1.75410514   5.16500971 50
#> 29        1             BC2 __ EP __ bcells  -3.76086815  14.46323277 50
#> 30        1            BC2 __ BC1 __ bcells  -2.04831400  -6.49826983 50
#> 31        1            BC2 __ BC3 __ bcells   1.60313412  -3.92883273 50
#> 32        1         BC2 __ TC_CD4 __ bcells  -7.69779151  12.91317577 50
#> 33        1         BC2 __ TC_CD8 __ bcells  -8.81546771   3.67014067 50
#> 34        1            BC2 __ MC1 __ bcells  -0.96692825  24.40344897 50
#> 35        1            BC2 __ MC2 __ bcells  -2.44582126  12.86126562 50
#> 36        1            BC2 __ MC3 __ bcells  -0.75965270   8.17839638 50
#> 37        1             BC2 __ GC __ bcells   4.47629354  22.94590620 50
#> 38        1      BC2 __ Undefined __ bcells   1.14403514   2.61505415 50
#> 39        1            BC3 __ SC1 __ bcells  -5.52417571  -2.13734635 50
#> 40        1            BC3 __ SC2 __ bcells   1.85945873   1.64482319 50
#> 41        1            BC3 __ SC3 __ bcells   0.02880508   1.35570737 50
#> 42        1            BC3 __ SC4 __ bcells   4.20463336   1.97419729 50
#> 43        1            BC3 __ SC5 __ bcells   2.75502898   1.02838878 50
#> 44        1            BC3 __ SC6 __ bcells  -8.22680811  -4.35737101 50
#> 45        1            BC3 __ SC7 __ bcells  -1.79813273  -0.10569195 50
#> 46        1            BC3 __ EC1 __ bcells -28.64214448 -16.86792784 50
#> 47        1            BC3 __ EC2 __ bcells  -3.83777070  -0.33471263 50
#> 48        1             BC3 __ EP __ bcells -25.64128965 -15.54988992 50
#> 49        1            BC3 __ BC1 __ bcells   1.34846170  -2.55275636 50
#> 50        1            BC3 __ BC2 __ bcells  -4.54167856  -1.74152224 50
#> 51        1         BC3 __ TC_CD4 __ bcells -24.39707984 -14.52579806 50
#> 52        1         BC3 __ TC_CD8 __ bcells -14.12486672  -9.82024776 50
#> 53        1            BC3 __ MC1 __ bcells -27.03143937 -17.14645521 50
#> 54        1            BC3 __ MC2 __ bcells -23.28819363 -14.57633285 50
#> 55        1            BC3 __ MC3 __ bcells -12.61905344  -6.99561139 50
#> 56        1             BC3 __ GC __ bcells -15.48135109  -6.60555103 50
#> 57        1      BC3 __ Undefined __ bcells  -2.55082643  -0.99511402 50
#> 58        1       EC1 __ SC1 __ endothelial   0.89249644  -8.21049644 50
#> 59        1       EC1 __ SC2 __ endothelial -12.82349442  -1.79222851 50
#> 60        1       EC1 __ SC3 __ endothelial -19.58186460   2.17910688 50
#> 61        1       EC1 __ SC4 __ endothelial -12.28477517 -13.93625878 50
#> 62        1       EC1 __ SC5 __ endothelial -16.47503365 -16.84608586 50
#> 63        1       EC1 __ SC6 __ endothelial  17.70862577  -0.80024435 50
#> 64        1       EC1 __ SC7 __ endothelial  -8.49638174  -5.60949837 50
#> 65        1       EC1 __ EC2 __ endothelial   6.23326241  -3.46252764 50
#> 66        1        EC1 __ EP __ endothelial  17.11138888   2.21443596 50
#> 67        1       EC1 __ BC1 __ endothelial -18.62994472 -20.62538726 50
#> 68        1       EC1 __ BC2 __ endothelial   6.27218402  -6.19513455 50
#> 69        1       EC1 __ BC3 __ endothelial -22.78738985 -11.05122645 50
#> 70        1    EC1 __ TC_CD4 __ endothelial  32.25440906  10.81589094 50
#> 71        1    EC1 __ TC_CD8 __ endothelial  22.10419636   7.00592236 50
#> 72        1       EC1 __ MC1 __ endothelial  43.20593237   9.87187333 50
#> 73        1       EC1 __ MC2 __ endothelial  20.56735298  -0.94555344 50
#> 74        1       EC1 __ MC3 __ endothelial  11.29317679  -4.08508330 50
#> 75        1        EC1 __ GC __ endothelial  37.07819869   4.42500731 50
#> 76        1 EC1 __ Undefined __ endothelial  -2.29358204  -5.21245332 50
#> 77        1       EC2 __ SC1 __ endothelial   1.40701867  -5.31845268 50
#> 78        1       EC2 __ SC2 __ endothelial  12.23284805  18.37710425 50
#> 79        1       EC2 __ SC3 __ endothelial  19.49022477  30.44259841 50
#> 80        1       EC2 __ SC4 __ endothelial   2.23712328   8.45822979 50
#> 81        1       EC2 __ SC5 __ endothelial  -8.93238185  -3.03885013 50
#> 82        1       EC2 __ SC6 __ endothelial   3.37261304  -8.22769141 50
#> 83        1       EC2 __ SC7 __ endothelial   5.07087158   9.52966590 50
#> 84        1       EC2 __ EC1 __ endothelial  -1.89968884 -28.99353217 50
#> 85        1        EC2 __ EP __ endothelial -11.38642364 -24.31311851 50
#> 86        1       EC2 __ BC1 __ endothelial -11.28472456  -1.73472791 50
#> 87        1       EC2 __ BC2 __ endothelial  -0.11983026  -8.39324194 50
#> 88        1       EC2 __ BC3 __ endothelial   0.51175392  13.07977773 50
#> 89        1    EC2 __ TC_CD4 __ endothelial  -6.62109281 -21.53590034 50
#> 90        1    EC2 __ TC_CD8 __ endothelial  -7.76523730 -20.36006248 50
#> 91        1       EC2 __ MC1 __ endothelial  -3.98117414 -27.81589823 50
#> 92        1       EC2 __ MC2 __ endothelial  -3.70200295 -19.19210543 50
#> 93        1       EC2 __ MC3 __ endothelial  -4.30573815 -15.34532752 50
#> 94        1        EC2 __ GC __ endothelial  10.83814189 -13.88624639 50
#> 95        1 EC2 __ Undefined __ endothelial  -1.49881017  -1.71717030 50
#> 96        1         EP __ SC1 __ epithelial   4.80544654   1.30747705 50
#> 97        1         EP __ SC2 __ epithelial -20.03691469  -6.20532646 50
#> 98        1         EP __ SC3 __ epithelial -23.13108667  -9.58779892 50
#> 99        1         EP __ SC4 __ epithelial -16.44095890  -7.09725059 50
#> 100       1         EP __ SC5 __ epithelial  -6.91236662  -0.54458276 50
#> 101       1         EP __ SC6 __ epithelial  -6.05117363   0.23308250 50
#> 102       1         EP __ SC7 __ epithelial -12.33129347  -1.93393505 50
#> 103       1         EP __ EC1 __ epithelial  10.77228179   1.36920506 50
#> 104       1         EP __ EC2 __ epithelial  -9.36165751   2.04007969 50
#> 105       1         EP __ BC1 __ epithelial   1.47910728  -4.47383729 50
#> 106       1         EP __ BC2 __ epithelial  -3.14814650  -1.00001008 50
#> 107       1         EP __ BC3 __ epithelial -22.47619522 -11.53386804 50
#> 108       1      EP __ TC_CD4 __ epithelial  24.89104546  -1.13182073 50
#> 109       1      EP __ TC_CD8 __ epithelial  12.53938564  -6.61528366 50
#> 110       1         EP __ MC1 __ epithelial  14.62724794   2.37702017 50
#> 111       1         EP __ MC2 __ epithelial  17.33972059   3.70697299 50
#> 112       1         EP __ MC3 __ epithelial   2.71234158   1.78500088 50
#> 113       1          EP __ GC __ epithelial -11.50083291   3.70668460 50
#> 114       1   EP __ Undefined __ epithelial  -6.70915260  -2.14155004 50
#> 115       1            BC1 __ SC1 __ immune   0.76301875   2.24784933 50
#> 116       1            BC1 __ SC2 __ immune  -7.47059261  -6.42629499 50
#> 117       1            BC1 __ SC3 __ immune  -9.37793451  -3.58368714 50
#> 118       1            BC1 __ SC4 __ immune   1.13997646  -0.23640936 50
#> 119       1            BC1 __ SC5 __ immune   6.92458926   5.34963911 50
#> 120       1            BC1 __ SC6 __ immune  -8.28486988  -9.57825808 50
#> 121       1            BC1 __ SC7 __ immune  -7.13642931  -6.80630021 50
#> 122       1            BC1 __ EC1 __ immune -24.57970886 -27.13905373 50
#> 123       1            BC1 __ EC2 __ immune -14.12189347 -13.79372020 50
#> 124       1             BC1 __ EP __ immune  -4.37129472  -1.07339197 50
#> 125       1            BC1 __ BC2 __ immune  -7.10583144  -8.93170309 50
#> 126       1            BC1 __ BC3 __ immune   1.88827295   0.15302397 50
#> 127       1         BC1 __ TC_CD4 __ immune -17.88982667 -18.01448774 50
#> 128       1         BC1 __ TC_CD8 __ immune  -6.91600512 -14.60395554 50
#> 129       1            BC1 __ MC1 __ immune -21.11848451 -24.86941500 50
#> 130       1            BC1 __ MC2 __ immune -13.70128934 -17.08739252 50
#> 131       1            BC1 __ MC3 __ immune  -8.44703838 -12.94582392 50
#> 132       1             BC1 __ GC __ immune -27.56957741 -31.02976607 50
#> 133       1      BC1 __ Undefined __ immune  -4.64746577  -5.39447349 50
#> 134       1            BC2 __ SC1 __ immune   1.82752333   2.33311295 50
#> 135       1            BC2 __ SC2 __ immune   2.45879059   6.35360744 50
#> 136       1            BC2 __ SC3 __ immune   1.35981727  11.05776029 50
#> 137       1            BC2 __ SC4 __ immune   1.05102750   0.59277936 50
#> 138       1            BC2 __ SC5 __ immune   0.43019776  -1.67206586 50
#> 139       1            BC2 __ SC6 __ immune   3.64561767   2.03798393 50
#> 140       1            BC2 __ SC7 __ immune   1.49766950   3.27971031 50
#> 141       1            BC2 __ EC1 __ immune  -0.23030303  -7.53946304 50
#> 142       1            BC2 __ EC2 __ immune   1.75410514   4.58157850 50
#> 143       1             BC2 __ EP __ immune  -3.76086815  -4.06452353 50
#> 144       1            BC2 __ BC1 __ immune  -2.04831400  -4.95253407 50
#> 145       1            BC2 __ BC3 __ immune   1.60313412   1.56540274 50
#> 146       1         BC2 __ TC_CD4 __ immune  -7.69779151 -10.62569471 50
#> 147       1         BC2 __ TC_CD8 __ immune  -8.81546771 -13.12728560 50
#> 148       1            BC2 __ MC1 __ immune  -0.96692825  -9.88661868 50
#> 149       1            BC2 __ MC2 __ immune  -2.44582126  -8.41085582 50
#> 150       1            BC2 __ MC3 __ immune  -0.75965270  -6.57995631 50
#> 151       1             BC2 __ GC __ immune   4.47629354  -3.47009309 50
#> 152       1      BC2 __ Undefined __ immune   1.14403514   0.38066180 50
#> 153       1            BC3 __ SC1 __ immune  -5.52417571  -4.50483867 50
#> 154       1            BC3 __ SC2 __ immune   1.85945873   5.15580021 50
#> 155       1            BC3 __ SC3 __ immune   0.02880508   9.35501008 50
#> 156       1            BC3 __ SC4 __ immune   4.20463336   3.86699301 50
#> 157       1            BC3 __ SC5 __ immune   2.75502898   0.82260998 50
#> 158       1            BC3 __ SC6 __ immune  -8.22680811  -8.51574826 50
#> 159       1            BC3 __ SC7 __ immune  -1.79813273   0.03541308 50
#> 160       1            BC3 __ EC1 __ immune -28.64214448 -30.35190083 50
#> 161       1            BC3 __ EC2 __ immune  -3.83777070  -0.21094300 50
#> 162       1             BC3 __ EP __ immune -25.64128965 -25.86454720 50
#> 163       1            BC3 __ BC1 __ immune   1.34846170  -1.83738117 50
#> 164       1            BC3 __ BC2 __ immune  -4.54167856  -4.81437040 50
#> 165       1         BC3 __ TC_CD4 __ immune -24.39707984 -25.05902103 50
#> 166       1         BC3 __ TC_CD8 __ immune -14.12486672 -21.46010220 50
#> 167       1            BC3 __ MC1 __ immune -27.03143937 -29.97295448 50
#> 168       1            BC3 __ MC2 __ immune -23.28819363 -25.46513441 50
#> 169       1            BC3 __ MC3 __ immune -12.61905344 -15.76394184 50
#> 170       1             BC3 __ GC __ immune -15.48135109 -18.87056329 50
#> 171       1      BC3 __ Undefined __ immune  -2.55082643  -3.04611362 50
#> 172       1             GC __ SC1 __ immune   6.77064569   8.10396635 50
#> 173       1             GC __ SC2 __ immune   7.71296408  14.17697573 50
#> 174       1             GC __ SC3 __ immune  -3.37866874   7.01696971 50
#> 175       1             GC __ SC4 __ immune   0.65056974   1.35095884 50
#> 176       1             GC __ SC5 __ immune  -7.44767874 -10.17928190 50
#> 177       1             GC __ SC6 __ immune  27.16485488  24.96069249 50
#> 178       1             GC __ SC7 __ immune   4.31369133   7.00866823 50
#> 179       1             GC __ EC1 __ immune  37.33786035  28.49763558 50
#> 180       1             GC __ EC2 __ immune  21.28458048  26.31268392 50
#> 181       1              GC __ EP __ immune  -7.94270959  -8.75869404 50
#> 182       1             GC __ BC1 __ immune -22.50909911 -24.24045168 50
#> 183       1             GC __ BC2 __ immune  11.61412993  10.03846711 50
#> 184       1             GC __ BC3 __ immune  -5.15873215  -3.23356614 50
#> 185       1          GC __ TC_CD4 __ immune  11.85533933   8.90564443 50
#> 186       1          GC __ TC_CD8 __ immune  -3.54011398  -8.49939131 50
#> 187       1             GC __ MC1 __ immune  36.00582772  23.55332502 50
#> 188       1             GC __ MC2 __ immune  24.37331770  16.94446964 50
#> 189       1             GC __ MC3 __ immune  10.24788540   3.53324147 50
#> 190       1       GC __ Undefined __ immune   1.48935520   1.13310430 50
#> 191       1            MC1 __ SC1 __ immune  -0.61199088  -0.30939253 50
#> 192       1            MC1 __ SC2 __ immune -18.28782268 -16.05879366 50
#> 193       1            MC1 __ SC3 __ immune -28.72926602 -23.39441345 50
#> 194       1            MC1 __ SC4 __ immune -14.67938623 -15.42549075 50
#> 195       1            MC1 __ SC5 __ immune -11.57467584 -14.05332935 50
#> 196       1            MC1 __ SC6 __ immune  15.68790061  11.18139646 50
#> 197       1            MC1 __ SC7 __ immune -11.60115101 -11.46469955 50
#> 198       1            MC1 __ EC1 __ immune  41.79440306  33.15475932 50
#> 199       1            MC1 __ EC2 __ immune   3.13886652   3.06165965 50
#> 200       1             MC1 __ EP __ immune  19.86734006  25.04653231 50
#> 201       1            MC1 __ BC1 __ immune -14.42068978 -15.55791269 50
#> 202       1            MC1 __ BC2 __ immune   4.10866102   0.96976402 50
#> 203       1            MC1 __ BC3 __ immune -21.27660144 -21.18400320 50
#> 204       1         MC1 __ TC_CD4 __ immune  35.13097923  30.73280337 50
#> 205       1         MC1 __ TC_CD8 __ immune  55.86763193  43.43126925 50
#> 206       1            MC1 __ MC2 __ immune  19.85220805  11.82840541 50
#> 207       1            MC1 __ MC3 __ immune  12.40238288   5.47613220 50
#> 208       1             MC1 __ GC __ immune  34.63337191  23.30877291 50
#> 209       1      MC1 __ Undefined __ immune  -4.80486453  -5.92047048 50
#> 210       1            MC2 __ SC1 __ immune   1.06151367   1.65403414 50
#> 211       1            MC2 __ SC2 __ immune  -7.48618623  -4.61299061 50
#> 212       1            MC2 __ SC3 __ immune -13.44381602  -5.73651588 50
#> 213       1            MC2 __ SC4 __ immune -11.85858353 -12.71517346 50
#> 214       1            MC2 __ SC5 __ immune  -2.67485404  -5.12145179 50
#> 215       1            MC2 __ SC6 __ immune   2.73453804  -0.64480572 50
#> 216       1            MC2 __ SC7 __ immune  -4.62776308  -4.08911010 50
#> 217       1            MC2 __ EC1 __ immune  17.88674016   9.11451207 50
#> 218       1            MC2 __ EC2 __ immune   1.71471389   4.85219130 50
#> 219       1             MC2 __ EP __ immune  21.41779254  26.47010719 50
#> 220       1            MC2 __ BC1 __ immune  -7.17227613  -9.06444397 50
#> 221       1            MC2 __ BC2 __ immune   0.83969087  -2.34449151 50
#> 222       1            MC2 __ BC3 __ immune -17.73344102 -18.35574415 50
#> 223       1         MC2 __ TC_CD4 __ immune   6.01881699   2.65769207 50
#> 224       1         MC2 __ TC_CD8 __ immune  -8.87427180 -14.92007105 50
#> 225       1            MC2 __ MC1 __ immune  18.52188109   7.01701560 50
#> 226       1            MC2 __ MC3 __ immune  20.99553414  12.53759687 50
#> 227       1             MC2 __ GC __ immune  21.76010100  11.35650491 50
#> 228       1      MC2 __ Undefined __ immune  -2.20803147  -3.43049828 50
#> 229       1            MC3 __ SC1 __ immune  -1.88441669  -0.71140935 50
#> 230       1            MC3 __ SC2 __ immune  -1.99867863   1.99095185 50
#> 231       1            MC3 __ SC3 __ immune  -8.48351416   0.18990561 50
#> 232       1            MC3 __ SC4 __ immune  -4.96962534  -5.31439937 50
#> 233       1            MC3 __ SC5 __ immune  -2.84783030  -4.74219383 50
#> 234       1            MC3 __ SC6 __ immune  -1.63585789  -3.83562345 50
#> 235       1            MC3 __ SC7 __ immune  -1.99929187  -0.50210562 50
#> 236       1            MC3 __ EC1 __ immune   6.09348568  -1.01485473 50
#> 237       1            MC3 __ EC2 __ immune  -1.43645202   1.16556550 50
#> 238       1             MC3 __ EP __ immune   2.98276254   5.62913101 50
#> 239       1            MC3 __ BC1 __ immune  -2.72155692  -5.31823231 50
#> 240       1            MC3 __ BC2 __ immune   0.27681570  -1.89121652 50
#> 241       1            MC3 __ BC3 __ immune  -6.72919978  -6.52601512 50
#> 242       1         MC3 __ TC_CD4 __ immune   6.16190963   3.70536315 50
#> 243       1         MC3 __ TC_CD8 __ immune   8.51663491   0.19401689 50
#> 244       1            MC3 __ MC1 __ immune   7.79631394  -1.05710461 50
#> 245       1            MC3 __ MC2 __ immune  17.59655567  10.18431649 50
#> 246       1             MC3 __ GC __ immune   4.99266512  -3.34365303 50
#> 247       1      MC3 __ Undefined __ immune  -0.22732766  -0.69599133 50
#> 248       1         TC_CD4 __ SC1 __ immune  -5.04625828  -4.87036888 50
#> 249       1         TC_CD4 __ SC2 __ immune -15.67442893 -15.45755675 50
#> 250       1         TC_CD4 __ SC3 __ immune -25.62331696 -23.33074997 50
#> 251       1         TC_CD4 __ SC4 __ immune -10.88705361 -11.86678936 50
#> 252       1         TC_CD4 __ SC5 __ immune -11.50459464 -13.47192842 50
#> 253       1         TC_CD4 __ SC6 __ immune   7.80160696   3.77406167 50
#> 254       1         TC_CD4 __ SC7 __ immune -11.34222531 -11.81513426 50
#> 255       1         TC_CD4 __ EC1 __ immune  28.16275891  18.70814834 50
#> 256       1         TC_CD4 __ EC2 __ immune  -1.54297389  -0.55044605 50
#> 257       1          TC_CD4 __ EP __ immune  28.99880148  32.35760844 50
#> 258       1         TC_CD4 __ BC1 __ immune -11.54152065 -13.04363202 50
#> 259       1         TC_CD4 __ BC2 __ immune  -4.51151169  -7.46525433 50
#> 260       1         TC_CD4 __ BC3 __ immune -18.22925554 -19.31205664 50
#> 261       1      TC_CD4 __ TC_CD8 __ immune  29.36567132  17.58980108 50
#> 262       1         TC_CD4 __ MC1 __ immune  32.16618047  19.56882097 50
#> 263       1         TC_CD4 __ MC2 __ immune   5.62490187  -0.98726972 50
#> 264       1         TC_CD4 __ MC3 __ immune   8.66623299   2.30613722 50
#> 265       1          TC_CD4 __ GC __ immune   9.71568692   1.15016121 50
#> 266       1   TC_CD4 __ Undefined __ immune  -3.39947564  -5.21752129 50
#> 267       1         TC_CD8 __ SC1 __ immune  -9.47822820  -7.40960441 50
#> 268       1         TC_CD8 __ SC2 __ immune -18.37087272 -17.51251376 50
#> 269       1         TC_CD8 __ SC3 __ immune -41.95090701 -41.39004326 50
#> 270       1         TC_CD8 __ SC4 __ immune -11.52492340 -13.80164727 50
#> 271       1         TC_CD8 __ SC5 __ immune -10.23247150 -11.45444054 50
#> 272       1         TC_CD8 __ SC6 __ immune  -5.67895435  -7.26386384 50
#> 273       1         TC_CD8 __ SC7 __ immune -21.20017974 -20.88808371 50
#> 274       1         TC_CD8 __ EC1 __ immune  17.11748036  15.50957677 50
#> 275       1         TC_CD8 __ EC2 __ immune  -4.08133697   0.26113117 50
#> 276       1          TC_CD8 __ EP __ immune  13.16438038  16.85815705 50
#> 277       1         TC_CD8 __ BC1 __ immune   0.58310032  -0.82456994 50
#> 278       1         TC_CD8 __ BC2 __ immune  -7.44912884  -5.62999949 50
#> 279       1         TC_CD8 __ BC3 __ immune  -7.48927069 -10.39408056 50
#> 280       1      TC_CD8 __ TC_CD4 __ immune  25.54401192  25.23435052 50
#> 281       1         TC_CD8 __ MC1 __ immune  47.93066557  39.51504009 50
#> 282       1         TC_CD8 __ MC2 __ immune -10.42877684 -11.97160143 50
#> 283       1         TC_CD8 __ MC3 __ immune   8.87556365   5.43239807 50
#> 284       1          TC_CD8 __ GC __ immune  -6.89374537 -10.40569802 50
#> 285       1   TC_CD8 __ Undefined __ immune  -2.28138533  -1.58818112 50
#> 286       1           MC1 __ SC1 __ myeloid  -0.61199088  -2.33326693 50
#> 287       1           MC1 __ SC2 __ myeloid -18.28782268  -6.52414712 50
#> 288       1           MC1 __ SC3 __ myeloid -28.72926602   2.27512124 50
#> 289       1           MC1 __ SC4 __ myeloid -14.67938623 -13.90727140 50
#> 290       1           MC1 __ SC5 __ myeloid -11.57467584 -13.65221196 50
#> 291       1           MC1 __ SC6 __ myeloid  15.68790061   0.50235123 50
#> 292       1           MC1 __ SC7 __ myeloid -11.60115101  -9.12771556 50
#> 293       1           MC1 __ EC1 __ myeloid  41.79440306  13.01601530 50
#> 294       1           MC1 __ EC2 __ myeloid   3.13886652  -0.78780897 50
#> 295       1            MC1 __ EP __ myeloid  19.86734006  11.33445772 50
#> 296       1           MC1 __ BC1 __ myeloid -14.42068978 -12.35317248 50
#> 297       1           MC1 __ BC2 __ myeloid   4.10866102  -6.05771774 50
#> 298       1           MC1 __ BC3 __ myeloid -21.27660144  -9.32849749 50
#> 299       1        MC1 __ TC_CD4 __ myeloid  35.13097923  12.52669355 50
#> 300       1        MC1 __ TC_CD8 __ myeloid  55.86763193  21.08709385 50
#> 301       1           MC1 __ MC2 __ myeloid  19.85220805  -0.50621968 50
#> 302       1           MC1 __ MC3 __ myeloid  12.40238288  -6.43363315 50
#> 303       1            MC1 __ GC __ myeloid  34.63337191   9.06402337 50
#> 304       1     MC1 __ Undefined __ myeloid  -4.80486453  -8.25646539 50
#> 305       1           MC2 __ SC1 __ myeloid   1.06151367  -1.10933323 50
#> 306       1           MC2 __ SC2 __ myeloid  -7.48618623   9.44945296 50
#> 307       1           MC2 __ SC3 __ myeloid -13.44381602  21.67069747 50
#> 308       1           MC2 __ SC4 __ myeloid -11.85858353  -8.66376289 50
#> 309       1           MC2 __ SC5 __ myeloid  -2.67485404  -7.35850933 50
#> 310       1           MC2 __ SC6 __ myeloid   2.73453804  -6.91194854 50
#> 311       1           MC2 __ SC7 __ myeloid  -4.62776308  -1.54469303 50
#> 312       1           MC2 __ EC1 __ myeloid  17.88674016  -8.50733501 50
#> 313       1           MC2 __ EC2 __ myeloid   1.71471389   8.92242116 50
#> 314       1            MC2 __ EP __ myeloid  21.41779254  11.70098074 50
#> 315       1           MC2 __ BC1 __ myeloid  -7.17227613  -9.29578661 50
#> 316       1           MC2 __ BC2 __ myeloid   0.83969087  -9.29986958 50
#> 317       1           MC2 __ BC3 __ myeloid -17.73344102 -10.49237710 50
#> 318       1        MC2 __ TC_CD4 __ myeloid   6.01881699 -10.33835630 50
#> 319       1        MC2 __ TC_CD8 __ myeloid  -8.87427180 -25.26369028 50
#> 320       1           MC2 __ MC1 __ myeloid  18.52188109  -8.70402812 50
#> 321       1           MC2 __ MC3 __ myeloid  20.99553414  -1.18574859 50
#> 322       1            MC2 __ GC __ myeloid  21.76010100  -0.63277353 50
#> 323       1     MC2 __ Undefined __ myeloid  -2.20803147  -5.97007909 50
#> 324       1           MC3 __ SC1 __ myeloid  -1.88441669  -4.48163740 50
#> 325       1           MC3 __ SC2 __ myeloid  -1.99867863  10.93802658 50
#> 326       1           MC3 __ SC3 __ myeloid  -8.48351416  20.60117526 50
#> 327       1           MC3 __ SC4 __ myeloid  -4.96962534  -2.62769747 50
#> 328       1           MC3 __ SC5 __ myeloid  -2.84783030  -5.02545527 50
#> 329       1           MC3 __ SC6 __ myeloid  -1.63585789 -11.60832994 50
#> 330       1           MC3 __ SC7 __ myeloid  -1.99929187   0.02050034 50
#> 331       1           MC3 __ EC1 __ myeloid   6.09348568 -18.60514729 50
#> 332       1           MC3 __ EC2 __ myeloid  -1.43645202  -0.53969066 50
#> 333       1            MC3 __ EP __ myeloid   2.98276254  -8.47057772 50
#> 334       1           MC3 __ BC1 __ myeloid  -2.72155692  -4.77995731 50
#> 335       1           MC3 __ BC2 __ myeloid   0.27681570  -9.09120272 50
#> 336       1           MC3 __ BC3 __ myeloid  -6.72919978   1.90159890 50
#> 337       1        MC3 __ TC_CD4 __ myeloid   6.16190963 -12.38979082 50
#> 338       1        MC3 __ TC_CD8 __ myeloid   8.51663491 -17.87928165 50
#> 339       1           MC3 __ MC1 __ myeloid   7.79631394 -19.39857978 50
#> 340       1           MC3 __ MC2 __ myeloid  17.59655567  -6.54449060 50
#> 341       1            MC3 __ GC __ myeloid   4.99266512 -17.83825055 50
#> 342       1     MC3 __ Undefined __ myeloid  -0.22732766  -3.74312682 50
#> 343       1         TC_CD4 __ SC1 __ tcells  -5.04625828  -2.09158018 50
#> 344       1         TC_CD4 __ SC2 __ tcells -15.67442893   9.70607525 50
#> 345       1         TC_CD4 __ SC3 __ tcells -25.62331696  16.20656281 50
#> 346       1         TC_CD4 __ SC4 __ tcells -10.88705361   4.33396989 50
#> 347       1         TC_CD4 __ SC5 __ tcells -11.50459464  -1.94470011 50
#> 348       1         TC_CD4 __ SC6 __ tcells   7.80160696   9.48627280 50
#> 349       1         TC_CD4 __ SC7 __ tcells -11.34222531   3.68269164 50
#> 350       1         TC_CD4 __ EC1 __ tcells  28.16275891   7.24811504 50
#> 351       1         TC_CD4 __ EC2 __ tcells  -1.54297389   8.14632842 50
#> 352       1          TC_CD4 __ EP __ tcells  28.99880148  -6.32202380 50
#> 353       1         TC_CD4 __ BC1 __ tcells -11.54152065  -7.02521577 50
#> 354       1         TC_CD4 __ BC2 __ tcells  -4.51151169  -9.48439522 50
#> 355       1         TC_CD4 __ BC3 __ tcells -18.22925554   2.62411322 50
#> 356       1      TC_CD4 __ TC_CD8 __ tcells  29.36567132 -19.56157487 50
#> 357       1         TC_CD4 __ MC1 __ tcells  32.16618047   0.81761053 50
#> 358       1         TC_CD4 __ MC2 __ tcells   5.62490187  -8.33419018 50
#> 359       1         TC_CD4 __ MC3 __ tcells   8.66623299  -2.84657643 50
#> 360       1          TC_CD4 __ GC __ tcells   9.71568692  19.33584125 50
#> 361       1   TC_CD4 __ Undefined __ tcells  -3.39947564  -4.15448064 50
#> 362       1         TC_CD8 __ SC1 __ tcells  -9.47822820 -12.85270588 50
#> 363       1         TC_CD8 __ SC2 __ tcells -18.37087272  -5.54935362 50
#> 364       1         TC_CD8 __ SC3 __ tcells -41.95090701 -41.75296799 50
#> 365       1         TC_CD8 __ SC4 __ tcells -11.52492340   2.50355589 50
#> 366       1         TC_CD8 __ SC5 __ tcells -10.23247150  -1.64376333 50
#> 367       1         TC_CD8 __ SC6 __ tcells  -5.67895435  -2.51033817 50
#> 368       1         TC_CD8 __ SC7 __ tcells -21.20017974 -12.25258522 50
#> 369       1         TC_CD8 __ EC1 __ tcells  17.11748036  -8.69834962 50
#> 370       1         TC_CD8 __ EC2 __ tcells  -4.08133697  -0.02245370 50
#> 371       1          TC_CD8 __ EP __ tcells  13.16438038 -20.40375242 50
#> 372       1         TC_CD8 __ BC1 __ tcells   0.58310032  12.11901502 50
#> 373       1         TC_CD8 __ BC2 __ tcells  -7.44912884 -19.18086439 50
#> 374       1         TC_CD8 __ BC3 __ tcells  -7.48927069  11.74641315 50
#> 375       1      TC_CD8 __ TC_CD4 __ tcells  25.54401192 -19.29338676 50
#> 376       1         TC_CD8 __ MC1 __ tcells  47.93066557   7.52460603 50
#> 377       1         TC_CD8 __ MC2 __ tcells -10.42877684 -18.20042804 50
#> 378       1         TC_CD8 __ MC3 __ tcells   8.87556365  -0.16387879 50
#> 379       1          TC_CD8 __ GC __ tcells  -6.89374537 -11.45263817 50
#> 380       1   TC_CD8 __ Undefined __ tcells  -2.28138533  -5.77125520 50
#> 381       1            EC1 __ SC1 __ tissue   0.89249644  -9.96570699 50
#> 382       1            EC1 __ SC2 __ tissue -12.82349442  17.00359922 50
#> 383       1            EC1 __ SC3 __ tissue -19.58186460  27.58729690 50
#> 384       1            EC1 __ SC4 __ tissue -12.28477517 -10.22482931 50
#> 385       1            EC1 __ SC5 __ tissue -16.47503365 -16.28448581 50
#> 386       1            EC1 __ SC6 __ tissue  17.70862577   2.35230526 50
#> 387       1            EC1 __ SC7 __ tissue  -8.49638174   5.06179905 50
#> 388       1            EC1 __ EC2 __ tissue   6.23326241   2.86896260 50
#> 389       1             EC1 __ EP __ tissue  17.11138888  -6.71926549 50
#> 390       1            EC1 __ BC1 __ tissue -18.62994472 -25.25419681 50
#> 391       1            EC1 __ BC2 __ tissue   6.27218402  -3.52096313 50
#> 392       1            EC1 __ BC3 __ tissue -22.78738985  -3.55551498 50
#> 393       1         EC1 __ TC_CD4 __ tissue  32.25440906   0.98384322 50
#> 394       1         EC1 __ TC_CD8 __ tissue  22.10419636  -5.91490896 50
#> 395       1            EC1 __ MC1 __ tissue  43.20593237  12.00836915 50
#> 396       1            EC1 __ MC2 __ tissue  20.56735298   2.58188258 50
#> 397       1            EC1 __ MC3 __ tissue  11.29317679  -2.48477411 50
#> 398       1             EC1 __ GC __ tissue  37.07819869  21.15172040 50
#> 399       1      EC1 __ Undefined __ tissue  -2.29358204  -1.61286598 50
#> 400       1            EC2 __ SC1 __ tissue   1.40701867  -2.71331156 50
#> 401       1            EC2 __ SC2 __ tissue  12.23284805  38.45577766 50
#> 402       1            EC2 __ SC3 __ tissue  19.49022477  57.38551565 50
#> 403       1            EC2 __ SC4 __ tissue   2.23712328  12.66029377 50
#> 404       1            EC2 __ SC5 __ tissue  -8.93238185  -8.44432936 50
#> 405       1            EC2 __ SC6 __ tissue   3.37261304   0.75818649 50
#> 406       1            EC2 __ SC7 __ tissue   5.07087158  19.82866027 50
#> 407       1            EC2 __ EC1 __ tissue  -1.89968884 -30.71976290 50
#> 408       1             EC2 __ EP __ tissue -11.38642364 -26.17023585 50
#> 409       1            EC2 __ BC1 __ tissue -11.28472456 -14.14992135 50
#> 410       1            EC2 __ BC2 __ tissue  -0.11983026  -3.64786387 50
#> 411       1            EC2 __ BC3 __ tissue   0.51175392  19.71376540 50
#> 412       1         EC2 __ TC_CD4 __ tissue  -6.62109281 -28.38563147 50
#> 413       1         EC2 __ TC_CD8 __ tissue  -7.76523730 -30.17120819 50
#> 414       1            EC2 __ MC1 __ tissue  -3.98117414 -29.38598249 50
#> 415       1            EC2 __ MC2 __ tissue  -3.70200295 -20.64156099 50
#> 416       1            EC2 __ MC3 __ tissue  -4.30573815 -11.62205548 50
#> 417       1             EC2 __ GC __ tissue  10.83814189  -1.43669702 50
#> 418       1      EC2 __ Undefined __ tissue  -1.49881017  -0.77588563 50
#> 419       1             EP __ SC1 __ tissue   4.80544654  -0.21618741 50
#> 420       1             EP __ SC2 __ tissue -20.03691469 -12.03080688 50
#> 421       1             EP __ SC3 __ tissue -23.13108667 -13.20046438 50
#> 422       1             EP __ SC4 __ tissue -16.44095890 -10.74879530 50
#> 423       1             EP __ SC5 __ tissue  -6.91236662  -4.11885583 50
#> 424       1             EP __ SC6 __ tissue  -6.05117363  -6.55739995 50
#> 425       1             EP __ SC7 __ tissue -12.33129347  -7.09398342 50
#> 426       1             EP __ EC1 __ tissue  10.77228179  -5.34978927 50
#> 427       1             EP __ EC2 __ tissue  -9.36165751  -5.19333713 50
#> 428       1             EP __ BC1 __ tissue   1.47910728  -0.38146656 50
#> 429       1             EP __ BC2 __ tissue  -3.14814650  -3.61724071 50
#> 430       1             EP __ BC3 __ tissue -22.47619522 -14.61809040 50
#> 431       1          EP __ TC_CD4 __ tissue  24.89104546   2.55352655 50
#> 432       1          EP __ TC_CD8 __ tissue  12.53938564  -3.23709641 50
#> 433       1             EP __ MC1 __ tissue  14.62724794  -1.94618871 50
#> 434       1             EP __ MC2 __ tissue  17.33972059   3.30590895 50
#> 435       1             EP __ MC3 __ tissue   2.71234158  -1.63565385 50
#> 436       1              EP __ GC __ tissue -11.50083291 -12.48007765 50
#> 437       1       EP __ Undefined __ tissue  -6.70915260  -4.14658796 50
#> 438       1            SC1 __ SC2 __ tumour   2.70262526  -5.24800623 50
#> 439       1            SC1 __ SC3 __ tumour   4.29462415  -7.25241009 50
#> 440       1            SC1 __ SC4 __ tumour  -0.37487456  -4.18778970 50
#> 441       1            SC1 __ SC5 __ tumour   1.31892673   0.91437085 50
#> 442       1            SC1 __ SC6 __ tumour   2.77131159   2.98075912 50
#> 443       1            SC1 __ SC7 __ tumour   0.48775945  -3.26948627 50
#> 444       1            SC1 __ EC1 __ tumour  -6.70104929  10.27271099 50
#> 445       1            SC1 __ EC2 __ tumour   1.09884717  -4.45463408 50
#> 446       1             SC1 __ EP __ tumour   1.83516605  23.59055820 50
#> 447       1            SC1 __ BC1 __ tumour   4.42292102   6.28354545 50
#> 448       1            SC1 __ BC2 __ tumour  -0.34736291   2.15135302 50
#> 449       1            SC1 __ BC3 __ tumour  -1.90098847  -5.97632198 50
#> 450       1         SC1 __ TC_CD4 __ tumour  -9.95399619   6.76434027 50
#> 451       1         SC1 __ TC_CD8 __ tumour -12.80172217   7.58419694 50
#> 452       1            SC1 __ MC1 __ tumour  -7.22108413  11.70426697 50
#> 453       1            SC1 __ MC2 __ tumour  -4.18624401   6.44400293 50
#> 454       1            SC1 __ MC3 __ tumour  -4.70561175   0.54103616 50
#> 455       1             SC1 __ GC __ tumour  -1.85061235   4.70950310 50
#> 456       1      SC1 __ Undefined __ tumour  -1.99823193   0.02108249 50
#> 457       1            SC2 __ SC1 __ tumour   1.42494300   0.80225303 50
#> 458       1            SC2 __ SC3 __ tumour  17.71757574   5.12258237 50
#> 459       1            SC2 __ SC4 __ tumour   3.88084540  -0.39441560 50
#> 460       1            SC2 __ SC5 __ tumour  -3.96720015  -3.40227652 50
#> 461       1            SC2 __ SC6 __ tumour   0.68569733  -0.45543768 50
#> 462       1            SC2 __ SC7 __ tumour   5.81360773   1.24950695 50
#> 463       1            SC2 __ EC1 __ tumour -19.12018112  -8.05288149 50
#> 464       1            SC2 __ EC2 __ tumour  10.23975697   3.00946844 50
#> 465       1             SC2 __ EP __ tumour -22.13211207  -6.36138328 50
#> 466       1            SC2 __ BC1 __ tumour  -5.47556298  -3.62391011 50
#> 467       1            SC2 __ BC2 __ tumour  -0.95005316  -0.78787681 50
#> 468       1            SC2 __ BC3 __ tumour   4.92301993   1.03341825 50
#> 469       1         SC2 __ TC_CD4 __ tumour -20.04080322 -10.01356277 50
#> 470       1         SC2 __ TC_CD8 __ tumour -21.74763044  -8.63078638 50
#> 471       1            SC2 __ MC1 __ tumour -23.14220392  -9.77797918 50
#> 472       1            SC2 __ MC2 __ tumour -12.84873370  -5.97149591 50
#> 473       1            SC2 __ MC3 __ tumour  -6.09707744  -1.11417648 50
#> 474       1             SC2 __ GC __ tumour  -2.55174244  -0.36098446 50
#> 475       1      SC2 __ Undefined __ tumour  -0.75497814   1.28770389 50
#> 476       1            SC3 __ SC1 __ tumour   3.15421549   2.98413613 50
#> 477       1            SC3 __ SC2 __ tumour  17.90669858   9.96954978 50
#> 478       1            SC3 __ SC4 __ tumour   0.55124105  -3.10038397 50
#> 479       1            SC3 __ SC5 __ tumour  -8.31569395  -7.64539534 50
#> 480       1            SC3 __ SC6 __ tumour   2.00868011   1.69150174 50
#> 481       1            SC3 __ SC7 __ tumour   9.39342226   4.98916643 50
#> 482       1            SC3 __ EC1 __ tumour -24.76666123 -20.30025243 50
#> 483       1            SC3 __ EC2 __ tumour  17.53342174  10.78493513 50
#> 484       1             SC3 __ EP __ tumour -25.16753453 -12.77013844 50
#> 485       1            SC3 __ BC1 __ tumour  -7.47358905  -5.38044687 50
#> 486       1            SC3 __ BC2 __ tumour  -1.88133010  -1.47484918 50
#> 487       1            SC3 __ BC3 __ tumour   3.14060508  -0.07097307 50
#> 488       1         SC3 __ TC_CD4 __ tumour -28.85903337 -22.74116698 50
#> 489       1         SC3 __ TC_CD8 __ tumour -42.78532350 -38.19751021 50
#> 490       1            SC3 __ MC1 __ tumour -31.85487571 -26.59383253 50
#> 491       1            SC3 __ MC2 __ tumour -17.93960428 -13.04987658 50
#> 492       1            SC3 __ MC3 __ tumour -11.91038661  -9.21426528 50
#> 493       1             SC3 __ GC __ tumour -11.50234210  -9.35740168 50
#> 494       1      SC3 __ Undefined __ tumour  -2.26375172  -0.92175261 50
#> 495       1            SC4 __ SC1 __ tumour  -3.43841056  -2.89599605 50
#> 496       1            SC4 __ SC2 __ tumour   1.69957671  -4.77984641 50
#> 497       1            SC4 __ SC3 __ tumour  -1.32544788 -10.42121658 50
#> 498       1            SC4 __ SC5 __ tumour   4.51383443   3.77323899 50
#> 499       1            SC4 __ SC6 __ tumour  -5.16257671  -4.74482554 50
#> 500       1            SC4 __ SC7 __ tumour  -2.46974506  -5.19771580 50
#> 501       1            SC4 __ EC1 __ tumour -19.79240556  -7.75902392 50
#> 502       1            SC4 __ EC2 __ tumour  -1.45834502  -5.60791671 50
#> 503       1             SC4 __ EP __ tumour -20.11711763  -6.25639461 50
#> 504       1            SC4 __ BC1 __ tumour   1.34839568   2.54668934 50
#> 505       1            SC4 __ BC2 __ tumour  -4.28221688  -2.45853584 50
#> 506       1            SC4 __ BC3 __ tumour   4.93981578   1.27945466 50
#> 507       1         SC4 __ TC_CD4 __ tumour -17.74011534  -4.40261121 50
#> 508       1         SC4 __ TC_CD8 __ tumour -16.68261112  -2.51118005 50
#> 509       1            SC4 __ MC1 __ tumour -21.34937488  -7.79153148 50
#> 510       1            SC4 __ MC2 __ tumour -18.23238122  -9.49204348 50
#> 511       1            SC4 __ MC3 __ tumour -10.27632124  -5.24046558 50
#> 512       1             SC4 __ GC __ tumour -10.19655796  -4.40736435 50
#> 513       1      SC4 __ Undefined __ tumour  -4.08904946  -1.67930965 50
#> 514       1            SC5 __ SC1 __ tumour  -2.29631456  -1.41889566 50
#> 515       1            SC5 __ SC2 __ tumour  -6.24626977 -10.63903391 50
#> 516       1            SC5 __ SC3 __ tumour -10.38099146 -17.29394686 50
#> 517       1            SC5 __ SC4 __ tumour   4.09319045   0.01432657 50
#> 518       1            SC5 __ SC6 __ tumour  -8.54692328  -7.77560923 50
#> 519       1            SC5 __ SC7 __ tumour  -5.13161756  -6.67050987 50
#> 520       1            SC5 __ EC1 __ tumour -23.12433564 -12.87233306 50
#> 521       1            SC5 __ EC2 __ tumour -12.21776939 -14.29230461 50
#> 522       1             SC5 __ EP __ tumour -11.73692210   4.42623852 50
#> 523       1            SC5 __ BC1 __ tumour   6.64012292   7.02279487 50
#> 524       1            SC5 __ BC2 __ tumour  -5.22638995  -3.28880799 50
#> 525       1            SC5 __ BC3 __ tumour   2.98228474  -0.46181230 50
#> 526       1         SC5 __ TC_CD4 __ tumour -18.33222559  -6.75456891 50
#> 527       1         SC5 __ TC_CD8 __ tumour -16.17948826  -2.70105755 50
#> 528       1            SC5 __ MC1 __ tumour -18.81051293  -5.68759627 50
#> 529       1            SC5 __ MC2 __ tumour -10.33166332  -0.51775424 50
#> 530       1            SC5 __ MC3 __ tumour  -8.65533289  -2.92517469 50
#> 531       1             SC5 __ GC __ tumour -16.16298238  -9.49132136 50
#> 532       1      SC5 __ Undefined __ tumour  -4.32296483  -1.79567475 50
#> 533       1            SC6 __ SC1 __ tumour   6.00999551   5.71853546 50
#> 534       1            SC6 __ SC2 __ tumour   5.18232774  -4.08227662 50
#> 535       1            SC6 __ SC3 __ tumour   6.53384694  -5.79062074 50
#> 536       1            SC6 __ SC4 __ tumour   0.96059463  -3.68199185 50
#> 537       1            SC6 __ SC5 __ tumour  -2.35478614  -3.49910962 50
#> 538       1            SC6 __ SC7 __ tumour   5.22418304   0.01346516 50
#> 539       1            SC6 __ EC1 __ tumour  11.00984799  37.25518686 50
#> 540       1            SC6 __ EC2 __ tumour   6.23210291   0.74301637 50
#> 541       1             SC6 __ EP __ tumour  -6.18035567  14.79005854 50
#> 542       1            SC6 __ BC1 __ tumour  -2.27026239  -1.97032973 50
#> 543       1            SC6 __ BC2 __ tumour   4.66935271   6.34034613 50
#> 544       1            SC6 __ BC3 __ tumour  -1.53176986  -7.06225502 50
#> 545       1         SC6 __ TC_CD4 __ tumour   4.93122368  32.37139082 50
#> 546       1         SC6 __ TC_CD8 __ tumour  -7.11759809  14.97776834 50
#> 547       1            SC6 __ MC1 __ tumour  10.14211680  39.95144154 50
#> 548       1            SC6 __ MC2 __ tumour  -0.29926389  12.35075729 50
#> 549       1            SC6 __ MC3 __ tumour  -1.92409747   5.78073971 50
#> 550       1             SC6 __ GC __ tumour  19.14291979  28.61781957 50
#> 551       1      SC6 __ Undefined __ tumour  -0.51077532   0.96766790 50
#> 552       1            SC7 __ SC1 __ tumour   0.82026448   0.41024275 50
#> 553       1            SC7 __ SC2 __ tumour   7.55491137  -1.35211911 50
#> 554       1            SC7 __ SC3 __ tumour  11.04658693  -2.05230671 50
#> 555       1            SC7 __ SC4 __ tumour   0.90724982  -3.14470640 50
#> 556       1            SC7 __ SC5 __ tumour  -1.40468434  -1.13303511 50
#> 557       1            SC7 __ SC6 __ tumour   2.24589480   1.29483287 50
#> 558       1            SC7 __ EC1 __ tumour -14.40582242  -1.00102642 50
#> 559       1            SC7 __ EC2 __ tumour   4.96726133  -2.01797287 50
#> 560       1             SC7 __ EP __ tumour -13.99256016   3.81255541 50
#> 561       1            SC7 __ BC1 __ tumour  -3.78037946  -1.78010867 50
#> 562       1            SC7 __ BC2 __ tumour  -0.28388005   0.82743389 50
#> 563       1            SC7 __ BC3 __ tumour   2.58845126  -1.24811380 50
#> 564       1         SC7 __ TC_CD4 __ tumour -15.53187685  -2.32834041 50
#> 565       1         SC7 __ TC_CD8 __ tumour -23.40164997 -10.50225092 50
#> 566       1            SC7 __ MC1 __ tumour -16.42572805  -0.96610895 50
#> 567       1            SC7 __ MC2 __ tumour  -9.08760291   0.18139636 50
#> 568       1            SC7 __ MC3 __ tumour  -4.61365500   1.21569810 50
#> 569       1             SC7 __ GC __ tumour  -3.72628680   1.04248826 50
#> 570       1      SC7 __ Undefined __ tumour   0.68060043   2.82581557 50
#>     weightQuantile inhom  edge includeZeroCells window window.length
#> 1              0.8  TRUE FALSE             TRUE convex            NA
#> 2              0.8  TRUE FALSE             TRUE convex            NA
#> 3              0.8  TRUE FALSE             TRUE convex            NA
#> 4              0.8  TRUE FALSE             TRUE convex            NA
#> 5              0.8  TRUE FALSE             TRUE convex            NA
#> 6              0.8  TRUE FALSE             TRUE convex            NA
#> 7              0.8  TRUE FALSE             TRUE convex            NA
#> 8              0.8  TRUE FALSE             TRUE convex            NA
#> 9              0.8  TRUE FALSE             TRUE convex            NA
#> 10             0.8  TRUE FALSE             TRUE convex            NA
#> 11             0.8  TRUE FALSE             TRUE convex            NA
#> 12             0.8  TRUE FALSE             TRUE convex            NA
#> 13             0.8  TRUE FALSE             TRUE convex            NA
#> 14             0.8  TRUE FALSE             TRUE convex            NA
#> 15             0.8  TRUE FALSE             TRUE convex            NA
#> 16             0.8  TRUE FALSE             TRUE convex            NA
#> 17             0.8  TRUE FALSE             TRUE convex            NA
#> 18             0.8  TRUE FALSE             TRUE convex            NA
#> 19             0.8  TRUE FALSE             TRUE convex            NA
#> 20             0.8  TRUE FALSE             TRUE convex            NA
#> 21             0.8  TRUE FALSE             TRUE convex            NA
#> 22             0.8  TRUE FALSE             TRUE convex            NA
#> 23             0.8  TRUE FALSE             TRUE convex            NA
#> 24             0.8  TRUE FALSE             TRUE convex            NA
#> 25             0.8  TRUE FALSE             TRUE convex            NA
#> 26             0.8  TRUE FALSE             TRUE convex            NA
#> 27             0.8  TRUE FALSE             TRUE convex            NA
#> 28             0.8  TRUE FALSE             TRUE convex            NA
#> 29             0.8  TRUE FALSE             TRUE convex            NA
#> 30             0.8  TRUE FALSE             TRUE convex            NA
#> 31             0.8  TRUE FALSE             TRUE convex            NA
#> 32             0.8  TRUE FALSE             TRUE convex            NA
#> 33             0.8  TRUE FALSE             TRUE convex            NA
#> 34             0.8  TRUE FALSE             TRUE convex            NA
#> 35             0.8  TRUE FALSE             TRUE convex            NA
#> 36             0.8  TRUE FALSE             TRUE convex            NA
#> 37             0.8  TRUE FALSE             TRUE convex            NA
#> 38             0.8  TRUE FALSE             TRUE convex            NA
#> 39             0.8  TRUE FALSE             TRUE convex            NA
#> 40             0.8  TRUE FALSE             TRUE convex            NA
#> 41             0.8  TRUE FALSE             TRUE convex            NA
#> 42             0.8  TRUE FALSE             TRUE convex            NA
#> 43             0.8  TRUE FALSE             TRUE convex            NA
#> 44             0.8  TRUE FALSE             TRUE convex            NA
#> 45             0.8  TRUE FALSE             TRUE convex            NA
#> 46             0.8  TRUE FALSE             TRUE convex            NA
#> 47             0.8  TRUE FALSE             TRUE convex            NA
#> 48             0.8  TRUE FALSE             TRUE convex            NA
#> 49             0.8  TRUE FALSE             TRUE convex            NA
#> 50             0.8  TRUE FALSE             TRUE convex            NA
#> 51             0.8  TRUE FALSE             TRUE convex            NA
#> 52             0.8  TRUE FALSE             TRUE convex            NA
#> 53             0.8  TRUE FALSE             TRUE convex            NA
#> 54             0.8  TRUE FALSE             TRUE convex            NA
#> 55             0.8  TRUE FALSE             TRUE convex            NA
#> 56             0.8  TRUE FALSE             TRUE convex            NA
#> 57             0.8  TRUE FALSE             TRUE convex            NA
#> 58             0.8  TRUE FALSE             TRUE convex            NA
#> 59             0.8  TRUE FALSE             TRUE convex            NA
#> 60             0.8  TRUE FALSE             TRUE convex            NA
#> 61             0.8  TRUE FALSE             TRUE convex            NA
#> 62             0.8  TRUE FALSE             TRUE convex            NA
#> 63             0.8  TRUE FALSE             TRUE convex            NA
#> 64             0.8  TRUE FALSE             TRUE convex            NA
#> 65             0.8  TRUE FALSE             TRUE convex            NA
#> 66             0.8  TRUE FALSE             TRUE convex            NA
#> 67             0.8  TRUE FALSE             TRUE convex            NA
#> 68             0.8  TRUE FALSE             TRUE convex            NA
#> 69             0.8  TRUE FALSE             TRUE convex            NA
#> 70             0.8  TRUE FALSE             TRUE convex            NA
#> 71             0.8  TRUE FALSE             TRUE convex            NA
#> 72             0.8  TRUE FALSE             TRUE convex            NA
#> 73             0.8  TRUE FALSE             TRUE convex            NA
#> 74             0.8  TRUE FALSE             TRUE convex            NA
#> 75             0.8  TRUE FALSE             TRUE convex            NA
#> 76             0.8  TRUE FALSE             TRUE convex            NA
#> 77             0.8  TRUE FALSE             TRUE convex            NA
#> 78             0.8  TRUE FALSE             TRUE convex            NA
#> 79             0.8  TRUE FALSE             TRUE convex            NA
#> 80             0.8  TRUE FALSE             TRUE convex            NA
#> 81             0.8  TRUE FALSE             TRUE convex            NA
#> 82             0.8  TRUE FALSE             TRUE convex            NA
#> 83             0.8  TRUE FALSE             TRUE convex            NA
#> 84             0.8  TRUE FALSE             TRUE convex            NA
#> 85             0.8  TRUE FALSE             TRUE convex            NA
#> 86             0.8  TRUE FALSE             TRUE convex            NA
#> 87             0.8  TRUE FALSE             TRUE convex            NA
#> 88             0.8  TRUE FALSE             TRUE convex            NA
#> 89             0.8  TRUE FALSE             TRUE convex            NA
#> 90             0.8  TRUE FALSE             TRUE convex            NA
#> 91             0.8  TRUE FALSE             TRUE convex            NA
#> 92             0.8  TRUE FALSE             TRUE convex            NA
#> 93             0.8  TRUE FALSE             TRUE convex            NA
#> 94             0.8  TRUE FALSE             TRUE convex            NA
#> 95             0.8  TRUE FALSE             TRUE convex            NA
#> 96             0.8  TRUE FALSE             TRUE convex            NA
#> 97             0.8  TRUE FALSE             TRUE convex            NA
#> 98             0.8  TRUE FALSE             TRUE convex            NA
#> 99             0.8  TRUE FALSE             TRUE convex            NA
#> 100            0.8  TRUE FALSE             TRUE convex            NA
#> 101            0.8  TRUE FALSE             TRUE convex            NA
#> 102            0.8  TRUE FALSE             TRUE convex            NA
#> 103            0.8  TRUE FALSE             TRUE convex            NA
#> 104            0.8  TRUE FALSE             TRUE convex            NA
#> 105            0.8  TRUE FALSE             TRUE convex            NA
#> 106            0.8  TRUE FALSE             TRUE convex            NA
#> 107            0.8  TRUE FALSE             TRUE convex            NA
#> 108            0.8  TRUE FALSE             TRUE convex            NA
#> 109            0.8  TRUE FALSE             TRUE convex            NA
#> 110            0.8  TRUE FALSE             TRUE convex            NA
#> 111            0.8  TRUE FALSE             TRUE convex            NA
#> 112            0.8  TRUE FALSE             TRUE convex            NA
#> 113            0.8  TRUE FALSE             TRUE convex            NA
#> 114            0.8  TRUE FALSE             TRUE convex            NA
#> 115            0.8  TRUE FALSE             TRUE convex            NA
#> 116            0.8  TRUE FALSE             TRUE convex            NA
#> 117            0.8  TRUE FALSE             TRUE convex            NA
#> 118            0.8  TRUE FALSE             TRUE convex            NA
#> 119            0.8  TRUE FALSE             TRUE convex            NA
#> 120            0.8  TRUE FALSE             TRUE convex            NA
#> 121            0.8  TRUE FALSE             TRUE convex            NA
#> 122            0.8  TRUE FALSE             TRUE convex            NA
#> 123            0.8  TRUE FALSE             TRUE convex            NA
#> 124            0.8  TRUE FALSE             TRUE convex            NA
#> 125            0.8  TRUE FALSE             TRUE convex            NA
#> 126            0.8  TRUE FALSE             TRUE convex            NA
#> 127            0.8  TRUE FALSE             TRUE convex            NA
#> 128            0.8  TRUE FALSE             TRUE convex            NA
#> 129            0.8  TRUE FALSE             TRUE convex            NA
#> 130            0.8  TRUE FALSE             TRUE convex            NA
#> 131            0.8  TRUE FALSE             TRUE convex            NA
#> 132            0.8  TRUE FALSE             TRUE convex            NA
#> 133            0.8  TRUE FALSE             TRUE convex            NA
#> 134            0.8  TRUE FALSE             TRUE convex            NA
#> 135            0.8  TRUE FALSE             TRUE convex            NA
#> 136            0.8  TRUE FALSE             TRUE convex            NA
#> 137            0.8  TRUE FALSE             TRUE convex            NA
#> 138            0.8  TRUE FALSE             TRUE convex            NA
#> 139            0.8  TRUE FALSE             TRUE convex            NA
#> 140            0.8  TRUE FALSE             TRUE convex            NA
#> 141            0.8  TRUE FALSE             TRUE convex            NA
#> 142            0.8  TRUE FALSE             TRUE convex            NA
#> 143            0.8  TRUE FALSE             TRUE convex            NA
#> 144            0.8  TRUE FALSE             TRUE convex            NA
#> 145            0.8  TRUE FALSE             TRUE convex            NA
#> 146            0.8  TRUE FALSE             TRUE convex            NA
#> 147            0.8  TRUE FALSE             TRUE convex            NA
#> 148            0.8  TRUE FALSE             TRUE convex            NA
#> 149            0.8  TRUE FALSE             TRUE convex            NA
#> 150            0.8  TRUE FALSE             TRUE convex            NA
#> 151            0.8  TRUE FALSE             TRUE convex            NA
#> 152            0.8  TRUE FALSE             TRUE convex            NA
#> 153            0.8  TRUE FALSE             TRUE convex            NA
#> 154            0.8  TRUE FALSE             TRUE convex            NA
#> 155            0.8  TRUE FALSE             TRUE convex            NA
#> 156            0.8  TRUE FALSE             TRUE convex            NA
#> 157            0.8  TRUE FALSE             TRUE convex            NA
#> 158            0.8  TRUE FALSE             TRUE convex            NA
#> 159            0.8  TRUE FALSE             TRUE convex            NA
#> 160            0.8  TRUE FALSE             TRUE convex            NA
#> 161            0.8  TRUE FALSE             TRUE convex            NA
#> 162            0.8  TRUE FALSE             TRUE convex            NA
#> 163            0.8  TRUE FALSE             TRUE convex            NA
#> 164            0.8  TRUE FALSE             TRUE convex            NA
#> 165            0.8  TRUE FALSE             TRUE convex            NA
#> 166            0.8  TRUE FALSE             TRUE convex            NA
#> 167            0.8  TRUE FALSE             TRUE convex            NA
#> 168            0.8  TRUE FALSE             TRUE convex            NA
#> 169            0.8  TRUE FALSE             TRUE convex            NA
#> 170            0.8  TRUE FALSE             TRUE convex            NA
#> 171            0.8  TRUE FALSE             TRUE convex            NA
#> 172            0.8  TRUE FALSE             TRUE convex            NA
#> 173            0.8  TRUE FALSE             TRUE convex            NA
#> 174            0.8  TRUE FALSE             TRUE convex            NA
#> 175            0.8  TRUE FALSE             TRUE convex            NA
#> 176            0.8  TRUE FALSE             TRUE convex            NA
#> 177            0.8  TRUE FALSE             TRUE convex            NA
#> 178            0.8  TRUE FALSE             TRUE convex            NA
#> 179            0.8  TRUE FALSE             TRUE convex            NA
#> 180            0.8  TRUE FALSE             TRUE convex            NA
#> 181            0.8  TRUE FALSE             TRUE convex            NA
#> 182            0.8  TRUE FALSE             TRUE convex            NA
#> 183            0.8  TRUE FALSE             TRUE convex            NA
#> 184            0.8  TRUE FALSE             TRUE convex            NA
#> 185            0.8  TRUE FALSE             TRUE convex            NA
#> 186            0.8  TRUE FALSE             TRUE convex            NA
#> 187            0.8  TRUE FALSE             TRUE convex            NA
#> 188            0.8  TRUE FALSE             TRUE convex            NA
#> 189            0.8  TRUE FALSE             TRUE convex            NA
#> 190            0.8  TRUE FALSE             TRUE convex            NA
#> 191            0.8  TRUE FALSE             TRUE convex            NA
#> 192            0.8  TRUE FALSE             TRUE convex            NA
#> 193            0.8  TRUE FALSE             TRUE convex            NA
#> 194            0.8  TRUE FALSE             TRUE convex            NA
#> 195            0.8  TRUE FALSE             TRUE convex            NA
#> 196            0.8  TRUE FALSE             TRUE convex            NA
#> 197            0.8  TRUE FALSE             TRUE convex            NA
#> 198            0.8  TRUE FALSE             TRUE convex            NA
#> 199            0.8  TRUE FALSE             TRUE convex            NA
#> 200            0.8  TRUE FALSE             TRUE convex            NA
#> 201            0.8  TRUE FALSE             TRUE convex            NA
#> 202            0.8  TRUE FALSE             TRUE convex            NA
#> 203            0.8  TRUE FALSE             TRUE convex            NA
#> 204            0.8  TRUE FALSE             TRUE convex            NA
#> 205            0.8  TRUE FALSE             TRUE convex            NA
#> 206            0.8  TRUE FALSE             TRUE convex            NA
#> 207            0.8  TRUE FALSE             TRUE convex            NA
#> 208            0.8  TRUE FALSE             TRUE convex            NA
#> 209            0.8  TRUE FALSE             TRUE convex            NA
#> 210            0.8  TRUE FALSE             TRUE convex            NA
#> 211            0.8  TRUE FALSE             TRUE convex            NA
#> 212            0.8  TRUE FALSE             TRUE convex            NA
#> 213            0.8  TRUE FALSE             TRUE convex            NA
#> 214            0.8  TRUE FALSE             TRUE convex            NA
#> 215            0.8  TRUE FALSE             TRUE convex            NA
#> 216            0.8  TRUE FALSE             TRUE convex            NA
#> 217            0.8  TRUE FALSE             TRUE convex            NA
#> 218            0.8  TRUE FALSE             TRUE convex            NA
#> 219            0.8  TRUE FALSE             TRUE convex            NA
#> 220            0.8  TRUE FALSE             TRUE convex            NA
#> 221            0.8  TRUE FALSE             TRUE convex            NA
#> 222            0.8  TRUE FALSE             TRUE convex            NA
#> 223            0.8  TRUE FALSE             TRUE convex            NA
#> 224            0.8  TRUE FALSE             TRUE convex            NA
#> 225            0.8  TRUE FALSE             TRUE convex            NA
#> 226            0.8  TRUE FALSE             TRUE convex            NA
#> 227            0.8  TRUE FALSE             TRUE convex            NA
#> 228            0.8  TRUE FALSE             TRUE convex            NA
#> 229            0.8  TRUE FALSE             TRUE convex            NA
#> 230            0.8  TRUE FALSE             TRUE convex            NA
#> 231            0.8  TRUE FALSE             TRUE convex            NA
#> 232            0.8  TRUE FALSE             TRUE convex            NA
#> 233            0.8  TRUE FALSE             TRUE convex            NA
#> 234            0.8  TRUE FALSE             TRUE convex            NA
#> 235            0.8  TRUE FALSE             TRUE convex            NA
#> 236            0.8  TRUE FALSE             TRUE convex            NA
#> 237            0.8  TRUE FALSE             TRUE convex            NA
#> 238            0.8  TRUE FALSE             TRUE convex            NA
#> 239            0.8  TRUE FALSE             TRUE convex            NA
#> 240            0.8  TRUE FALSE             TRUE convex            NA
#> 241            0.8  TRUE FALSE             TRUE convex            NA
#> 242            0.8  TRUE FALSE             TRUE convex            NA
#> 243            0.8  TRUE FALSE             TRUE convex            NA
#> 244            0.8  TRUE FALSE             TRUE convex            NA
#> 245            0.8  TRUE FALSE             TRUE convex            NA
#> 246            0.8  TRUE FALSE             TRUE convex            NA
#> 247            0.8  TRUE FALSE             TRUE convex            NA
#> 248            0.8  TRUE FALSE             TRUE convex            NA
#> 249            0.8  TRUE FALSE             TRUE convex            NA
#> 250            0.8  TRUE FALSE             TRUE convex            NA
#> 251            0.8  TRUE FALSE             TRUE convex            NA
#> 252            0.8  TRUE FALSE             TRUE convex            NA
#> 253            0.8  TRUE FALSE             TRUE convex            NA
#> 254            0.8  TRUE FALSE             TRUE convex            NA
#> 255            0.8  TRUE FALSE             TRUE convex            NA
#> 256            0.8  TRUE FALSE             TRUE convex            NA
#> 257            0.8  TRUE FALSE             TRUE convex            NA
#> 258            0.8  TRUE FALSE             TRUE convex            NA
#> 259            0.8  TRUE FALSE             TRUE convex            NA
#> 260            0.8  TRUE FALSE             TRUE convex            NA
#> 261            0.8  TRUE FALSE             TRUE convex            NA
#> 262            0.8  TRUE FALSE             TRUE convex            NA
#> 263            0.8  TRUE FALSE             TRUE convex            NA
#> 264            0.8  TRUE FALSE             TRUE convex            NA
#> 265            0.8  TRUE FALSE             TRUE convex            NA
#> 266            0.8  TRUE FALSE             TRUE convex            NA
#> 267            0.8  TRUE FALSE             TRUE convex            NA
#> 268            0.8  TRUE FALSE             TRUE convex            NA
#> 269            0.8  TRUE FALSE             TRUE convex            NA
#> 270            0.8  TRUE FALSE             TRUE convex            NA
#> 271            0.8  TRUE FALSE             TRUE convex            NA
#> 272            0.8  TRUE FALSE             TRUE convex            NA
#> 273            0.8  TRUE FALSE             TRUE convex            NA
#> 274            0.8  TRUE FALSE             TRUE convex            NA
#> 275            0.8  TRUE FALSE             TRUE convex            NA
#> 276            0.8  TRUE FALSE             TRUE convex            NA
#> 277            0.8  TRUE FALSE             TRUE convex            NA
#> 278            0.8  TRUE FALSE             TRUE convex            NA
#> 279            0.8  TRUE FALSE             TRUE convex            NA
#> 280            0.8  TRUE FALSE             TRUE convex            NA
#> 281            0.8  TRUE FALSE             TRUE convex            NA
#> 282            0.8  TRUE FALSE             TRUE convex            NA
#> 283            0.8  TRUE FALSE             TRUE convex            NA
#> 284            0.8  TRUE FALSE             TRUE convex            NA
#> 285            0.8  TRUE FALSE             TRUE convex            NA
#> 286            0.8  TRUE FALSE             TRUE convex            NA
#> 287            0.8  TRUE FALSE             TRUE convex            NA
#> 288            0.8  TRUE FALSE             TRUE convex            NA
#> 289            0.8  TRUE FALSE             TRUE convex            NA
#> 290            0.8  TRUE FALSE             TRUE convex            NA
#> 291            0.8  TRUE FALSE             TRUE convex            NA
#> 292            0.8  TRUE FALSE             TRUE convex            NA
#> 293            0.8  TRUE FALSE             TRUE convex            NA
#> 294            0.8  TRUE FALSE             TRUE convex            NA
#> 295            0.8  TRUE FALSE             TRUE convex            NA
#> 296            0.8  TRUE FALSE             TRUE convex            NA
#> 297            0.8  TRUE FALSE             TRUE convex            NA
#> 298            0.8  TRUE FALSE             TRUE convex            NA
#> 299            0.8  TRUE FALSE             TRUE convex            NA
#> 300            0.8  TRUE FALSE             TRUE convex            NA
#> 301            0.8  TRUE FALSE             TRUE convex            NA
#> 302            0.8  TRUE FALSE             TRUE convex            NA
#> 303            0.8  TRUE FALSE             TRUE convex            NA
#> 304            0.8  TRUE FALSE             TRUE convex            NA
#> 305            0.8  TRUE FALSE             TRUE convex            NA
#> 306            0.8  TRUE FALSE             TRUE convex            NA
#> 307            0.8  TRUE FALSE             TRUE convex            NA
#> 308            0.8  TRUE FALSE             TRUE convex            NA
#> 309            0.8  TRUE FALSE             TRUE convex            NA
#> 310            0.8  TRUE FALSE             TRUE convex            NA
#> 311            0.8  TRUE FALSE             TRUE convex            NA
#> 312            0.8  TRUE FALSE             TRUE convex            NA
#> 313            0.8  TRUE FALSE             TRUE convex            NA
#> 314            0.8  TRUE FALSE             TRUE convex            NA
#> 315            0.8  TRUE FALSE             TRUE convex            NA
#> 316            0.8  TRUE FALSE             TRUE convex            NA
#> 317            0.8  TRUE FALSE             TRUE convex            NA
#> 318            0.8  TRUE FALSE             TRUE convex            NA
#> 319            0.8  TRUE FALSE             TRUE convex            NA
#> 320            0.8  TRUE FALSE             TRUE convex            NA
#> 321            0.8  TRUE FALSE             TRUE convex            NA
#> 322            0.8  TRUE FALSE             TRUE convex            NA
#> 323            0.8  TRUE FALSE             TRUE convex            NA
#> 324            0.8  TRUE FALSE             TRUE convex            NA
#> 325            0.8  TRUE FALSE             TRUE convex            NA
#> 326            0.8  TRUE FALSE             TRUE convex            NA
#> 327            0.8  TRUE FALSE             TRUE convex            NA
#> 328            0.8  TRUE FALSE             TRUE convex            NA
#> 329            0.8  TRUE FALSE             TRUE convex            NA
#> 330            0.8  TRUE FALSE             TRUE convex            NA
#> 331            0.8  TRUE FALSE             TRUE convex            NA
#> 332            0.8  TRUE FALSE             TRUE convex            NA
#> 333            0.8  TRUE FALSE             TRUE convex            NA
#> 334            0.8  TRUE FALSE             TRUE convex            NA
#> 335            0.8  TRUE FALSE             TRUE convex            NA
#> 336            0.8  TRUE FALSE             TRUE convex            NA
#> 337            0.8  TRUE FALSE             TRUE convex            NA
#> 338            0.8  TRUE FALSE             TRUE convex            NA
#> 339            0.8  TRUE FALSE             TRUE convex            NA
#> 340            0.8  TRUE FALSE             TRUE convex            NA
#> 341            0.8  TRUE FALSE             TRUE convex            NA
#> 342            0.8  TRUE FALSE             TRUE convex            NA
#> 343            0.8  TRUE FALSE             TRUE convex            NA
#> 344            0.8  TRUE FALSE             TRUE convex            NA
#> 345            0.8  TRUE FALSE             TRUE convex            NA
#> 346            0.8  TRUE FALSE             TRUE convex            NA
#> 347            0.8  TRUE FALSE             TRUE convex            NA
#> 348            0.8  TRUE FALSE             TRUE convex            NA
#> 349            0.8  TRUE FALSE             TRUE convex            NA
#> 350            0.8  TRUE FALSE             TRUE convex            NA
#> 351            0.8  TRUE FALSE             TRUE convex            NA
#> 352            0.8  TRUE FALSE             TRUE convex            NA
#> 353            0.8  TRUE FALSE             TRUE convex            NA
#> 354            0.8  TRUE FALSE             TRUE convex            NA
#> 355            0.8  TRUE FALSE             TRUE convex            NA
#> 356            0.8  TRUE FALSE             TRUE convex            NA
#> 357            0.8  TRUE FALSE             TRUE convex            NA
#> 358            0.8  TRUE FALSE             TRUE convex            NA
#> 359            0.8  TRUE FALSE             TRUE convex            NA
#> 360            0.8  TRUE FALSE             TRUE convex            NA
#> 361            0.8  TRUE FALSE             TRUE convex            NA
#> 362            0.8  TRUE FALSE             TRUE convex            NA
#> 363            0.8  TRUE FALSE             TRUE convex            NA
#> 364            0.8  TRUE FALSE             TRUE convex            NA
#> 365            0.8  TRUE FALSE             TRUE convex            NA
#> 366            0.8  TRUE FALSE             TRUE convex            NA
#> 367            0.8  TRUE FALSE             TRUE convex            NA
#> 368            0.8  TRUE FALSE             TRUE convex            NA
#> 369            0.8  TRUE FALSE             TRUE convex            NA
#> 370            0.8  TRUE FALSE             TRUE convex            NA
#> 371            0.8  TRUE FALSE             TRUE convex            NA
#> 372            0.8  TRUE FALSE             TRUE convex            NA
#> 373            0.8  TRUE FALSE             TRUE convex            NA
#> 374            0.8  TRUE FALSE             TRUE convex            NA
#> 375            0.8  TRUE FALSE             TRUE convex            NA
#> 376            0.8  TRUE FALSE             TRUE convex            NA
#> 377            0.8  TRUE FALSE             TRUE convex            NA
#> 378            0.8  TRUE FALSE             TRUE convex            NA
#> 379            0.8  TRUE FALSE             TRUE convex            NA
#> 380            0.8  TRUE FALSE             TRUE convex            NA
#> 381            0.8  TRUE FALSE             TRUE convex            NA
#> 382            0.8  TRUE FALSE             TRUE convex            NA
#> 383            0.8  TRUE FALSE             TRUE convex            NA
#> 384            0.8  TRUE FALSE             TRUE convex            NA
#> 385            0.8  TRUE FALSE             TRUE convex            NA
#> 386            0.8  TRUE FALSE             TRUE convex            NA
#> 387            0.8  TRUE FALSE             TRUE convex            NA
#> 388            0.8  TRUE FALSE             TRUE convex            NA
#> 389            0.8  TRUE FALSE             TRUE convex            NA
#> 390            0.8  TRUE FALSE             TRUE convex            NA
#> 391            0.8  TRUE FALSE             TRUE convex            NA
#> 392            0.8  TRUE FALSE             TRUE convex            NA
#> 393            0.8  TRUE FALSE             TRUE convex            NA
#> 394            0.8  TRUE FALSE             TRUE convex            NA
#> 395            0.8  TRUE FALSE             TRUE convex            NA
#> 396            0.8  TRUE FALSE             TRUE convex            NA
#> 397            0.8  TRUE FALSE             TRUE convex            NA
#> 398            0.8  TRUE FALSE             TRUE convex            NA
#> 399            0.8  TRUE FALSE             TRUE convex            NA
#> 400            0.8  TRUE FALSE             TRUE convex            NA
#> 401            0.8  TRUE FALSE             TRUE convex            NA
#> 402            0.8  TRUE FALSE             TRUE convex            NA
#> 403            0.8  TRUE FALSE             TRUE convex            NA
#> 404            0.8  TRUE FALSE             TRUE convex            NA
#> 405            0.8  TRUE FALSE             TRUE convex            NA
#> 406            0.8  TRUE FALSE             TRUE convex            NA
#> 407            0.8  TRUE FALSE             TRUE convex            NA
#> 408            0.8  TRUE FALSE             TRUE convex            NA
#> 409            0.8  TRUE FALSE             TRUE convex            NA
#> 410            0.8  TRUE FALSE             TRUE convex            NA
#> 411            0.8  TRUE FALSE             TRUE convex            NA
#> 412            0.8  TRUE FALSE             TRUE convex            NA
#> 413            0.8  TRUE FALSE             TRUE convex            NA
#> 414            0.8  TRUE FALSE             TRUE convex            NA
#> 415            0.8  TRUE FALSE             TRUE convex            NA
#> 416            0.8  TRUE FALSE             TRUE convex            NA
#> 417            0.8  TRUE FALSE             TRUE convex            NA
#> 418            0.8  TRUE FALSE             TRUE convex            NA
#> 419            0.8  TRUE FALSE             TRUE convex            NA
#> 420            0.8  TRUE FALSE             TRUE convex            NA
#> 421            0.8  TRUE FALSE             TRUE convex            NA
#> 422            0.8  TRUE FALSE             TRUE convex            NA
#> 423            0.8  TRUE FALSE             TRUE convex            NA
#> 424            0.8  TRUE FALSE             TRUE convex            NA
#> 425            0.8  TRUE FALSE             TRUE convex            NA
#> 426            0.8  TRUE FALSE             TRUE convex            NA
#> 427            0.8  TRUE FALSE             TRUE convex            NA
#> 428            0.8  TRUE FALSE             TRUE convex            NA
#> 429            0.8  TRUE FALSE             TRUE convex            NA
#> 430            0.8  TRUE FALSE             TRUE convex            NA
#> 431            0.8  TRUE FALSE             TRUE convex            NA
#> 432            0.8  TRUE FALSE             TRUE convex            NA
#> 433            0.8  TRUE FALSE             TRUE convex            NA
#> 434            0.8  TRUE FALSE             TRUE convex            NA
#> 435            0.8  TRUE FALSE             TRUE convex            NA
#> 436            0.8  TRUE FALSE             TRUE convex            NA
#> 437            0.8  TRUE FALSE             TRUE convex            NA
#> 438            0.8  TRUE FALSE             TRUE convex            NA
#> 439            0.8  TRUE FALSE             TRUE convex            NA
#> 440            0.8  TRUE FALSE             TRUE convex            NA
#> 441            0.8  TRUE FALSE             TRUE convex            NA
#> 442            0.8  TRUE FALSE             TRUE convex            NA
#> 443            0.8  TRUE FALSE             TRUE convex            NA
#> 444            0.8  TRUE FALSE             TRUE convex            NA
#> 445            0.8  TRUE FALSE             TRUE convex            NA
#> 446            0.8  TRUE FALSE             TRUE convex            NA
#> 447            0.8  TRUE FALSE             TRUE convex            NA
#> 448            0.8  TRUE FALSE             TRUE convex            NA
#> 449            0.8  TRUE FALSE             TRUE convex            NA
#> 450            0.8  TRUE FALSE             TRUE convex            NA
#> 451            0.8  TRUE FALSE             TRUE convex            NA
#> 452            0.8  TRUE FALSE             TRUE convex            NA
#> 453            0.8  TRUE FALSE             TRUE convex            NA
#> 454            0.8  TRUE FALSE             TRUE convex            NA
#> 455            0.8  TRUE FALSE             TRUE convex            NA
#> 456            0.8  TRUE FALSE             TRUE convex            NA
#> 457            0.8  TRUE FALSE             TRUE convex            NA
#> 458            0.8  TRUE FALSE             TRUE convex            NA
#> 459            0.8  TRUE FALSE             TRUE convex            NA
#> 460            0.8  TRUE FALSE             TRUE convex            NA
#> 461            0.8  TRUE FALSE             TRUE convex            NA
#> 462            0.8  TRUE FALSE             TRUE convex            NA
#> 463            0.8  TRUE FALSE             TRUE convex            NA
#> 464            0.8  TRUE FALSE             TRUE convex            NA
#> 465            0.8  TRUE FALSE             TRUE convex            NA
#> 466            0.8  TRUE FALSE             TRUE convex            NA
#> 467            0.8  TRUE FALSE             TRUE convex            NA
#> 468            0.8  TRUE FALSE             TRUE convex            NA
#> 469            0.8  TRUE FALSE             TRUE convex            NA
#> 470            0.8  TRUE FALSE             TRUE convex            NA
#> 471            0.8  TRUE FALSE             TRUE convex            NA
#> 472            0.8  TRUE FALSE             TRUE convex            NA
#> 473            0.8  TRUE FALSE             TRUE convex            NA
#> 474            0.8  TRUE FALSE             TRUE convex            NA
#> 475            0.8  TRUE FALSE             TRUE convex            NA
#> 476            0.8  TRUE FALSE             TRUE convex            NA
#> 477            0.8  TRUE FALSE             TRUE convex            NA
#> 478            0.8  TRUE FALSE             TRUE convex            NA
#> 479            0.8  TRUE FALSE             TRUE convex            NA
#> 480            0.8  TRUE FALSE             TRUE convex            NA
#> 481            0.8  TRUE FALSE             TRUE convex            NA
#> 482            0.8  TRUE FALSE             TRUE convex            NA
#> 483            0.8  TRUE FALSE             TRUE convex            NA
#> 484            0.8  TRUE FALSE             TRUE convex            NA
#> 485            0.8  TRUE FALSE             TRUE convex            NA
#> 486            0.8  TRUE FALSE             TRUE convex            NA
#> 487            0.8  TRUE FALSE             TRUE convex            NA
#> 488            0.8  TRUE FALSE             TRUE convex            NA
#> 489            0.8  TRUE FALSE             TRUE convex            NA
#> 490            0.8  TRUE FALSE             TRUE convex            NA
#> 491            0.8  TRUE FALSE             TRUE convex            NA
#> 492            0.8  TRUE FALSE             TRUE convex            NA
#> 493            0.8  TRUE FALSE             TRUE convex            NA
#> 494            0.8  TRUE FALSE             TRUE convex            NA
#> 495            0.8  TRUE FALSE             TRUE convex            NA
#> 496            0.8  TRUE FALSE             TRUE convex            NA
#> 497            0.8  TRUE FALSE             TRUE convex            NA
#> 498            0.8  TRUE FALSE             TRUE convex            NA
#> 499            0.8  TRUE FALSE             TRUE convex            NA
#> 500            0.8  TRUE FALSE             TRUE convex            NA
#> 501            0.8  TRUE FALSE             TRUE convex            NA
#> 502            0.8  TRUE FALSE             TRUE convex            NA
#> 503            0.8  TRUE FALSE             TRUE convex            NA
#> 504            0.8  TRUE FALSE             TRUE convex            NA
#> 505            0.8  TRUE FALSE             TRUE convex            NA
#> 506            0.8  TRUE FALSE             TRUE convex            NA
#> 507            0.8  TRUE FALSE             TRUE convex            NA
#> 508            0.8  TRUE FALSE             TRUE convex            NA
#> 509            0.8  TRUE FALSE             TRUE convex            NA
#> 510            0.8  TRUE FALSE             TRUE convex            NA
#> 511            0.8  TRUE FALSE             TRUE convex            NA
#> 512            0.8  TRUE FALSE             TRUE convex            NA
#> 513            0.8  TRUE FALSE             TRUE convex            NA
#> 514            0.8  TRUE FALSE             TRUE convex            NA
#> 515            0.8  TRUE FALSE             TRUE convex            NA
#> 516            0.8  TRUE FALSE             TRUE convex            NA
#> 517            0.8  TRUE FALSE             TRUE convex            NA
#> 518            0.8  TRUE FALSE             TRUE convex            NA
#> 519            0.8  TRUE FALSE             TRUE convex            NA
#> 520            0.8  TRUE FALSE             TRUE convex            NA
#> 521            0.8  TRUE FALSE             TRUE convex            NA
#> 522            0.8  TRUE FALSE             TRUE convex            NA
#> 523            0.8  TRUE FALSE             TRUE convex            NA
#> 524            0.8  TRUE FALSE             TRUE convex            NA
#> 525            0.8  TRUE FALSE             TRUE convex            NA
#> 526            0.8  TRUE FALSE             TRUE convex            NA
#> 527            0.8  TRUE FALSE             TRUE convex            NA
#> 528            0.8  TRUE FALSE             TRUE convex            NA
#> 529            0.8  TRUE FALSE             TRUE convex            NA
#> 530            0.8  TRUE FALSE             TRUE convex            NA
#> 531            0.8  TRUE FALSE             TRUE convex            NA
#> 532            0.8  TRUE FALSE             TRUE convex            NA
#> 533            0.8  TRUE FALSE             TRUE convex            NA
#> 534            0.8  TRUE FALSE             TRUE convex            NA
#> 535            0.8  TRUE FALSE             TRUE convex            NA
#> 536            0.8  TRUE FALSE             TRUE convex            NA
#> 537            0.8  TRUE FALSE             TRUE convex            NA
#> 538            0.8  TRUE FALSE             TRUE convex            NA
#> 539            0.8  TRUE FALSE             TRUE convex            NA
#> 540            0.8  TRUE FALSE             TRUE convex            NA
#> 541            0.8  TRUE FALSE             TRUE convex            NA
#> 542            0.8  TRUE FALSE             TRUE convex            NA
#> 543            0.8  TRUE FALSE             TRUE convex            NA
#> 544            0.8  TRUE FALSE             TRUE convex            NA
#> 545            0.8  TRUE FALSE             TRUE convex            NA
#> 546            0.8  TRUE FALSE             TRUE convex            NA
#> 547            0.8  TRUE FALSE             TRUE convex            NA
#> 548            0.8  TRUE FALSE             TRUE convex            NA
#> 549            0.8  TRUE FALSE             TRUE convex            NA
#> 550            0.8  TRUE FALSE             TRUE convex            NA
#> 551            0.8  TRUE FALSE             TRUE convex            NA
#> 552            0.8  TRUE FALSE             TRUE convex            NA
#> 553            0.8  TRUE FALSE             TRUE convex            NA
#> 554            0.8  TRUE FALSE             TRUE convex            NA
#> 555            0.8  TRUE FALSE             TRUE convex            NA
#> 556            0.8  TRUE FALSE             TRUE convex            NA
#> 557            0.8  TRUE FALSE             TRUE convex            NA
#> 558            0.8  TRUE FALSE             TRUE convex            NA
#> 559            0.8  TRUE FALSE             TRUE convex            NA
#> 560            0.8  TRUE FALSE             TRUE convex            NA
#> 561            0.8  TRUE FALSE             TRUE convex            NA
#> 562            0.8  TRUE FALSE             TRUE convex            NA
#> 563            0.8  TRUE FALSE             TRUE convex            NA
#> 564            0.8  TRUE FALSE             TRUE convex            NA
#> 565            0.8  TRUE FALSE             TRUE convex            NA
#> 566            0.8  TRUE FALSE             TRUE convex            NA
#> 567            0.8  TRUE FALSE             TRUE convex            NA
#> 568            0.8  TRUE FALSE             TRUE convex            NA
#> 569            0.8  TRUE FALSE             TRUE convex            NA
#> 570            0.8  TRUE FALSE             TRUE convex            NA

5 Simulation and RsCurve

Here we use simulationCompartment to create an image where the relationship between 2 cell types depends on a \(3^{rd}\) cell population. In the image below we see that tumour_cells and cd8_t_cells appear dispersed, however when this relationship is placed in context of the large dispersion between tumour_cells and all the other t_cells, now tumour_cells and cd8_t_cells appear localised.

set.seed(10)

#simulating images
simulation = simulateCompartment(includeTissue = FALSE)

#selecting image where a significant conditional relationship exists
conditionalImage = simulation$sig

#plotting image
ggplot(conditionalImage, aes(x = x, y = y, col = cellType)) +
    geom_point()

The rsCurve function plots the L-function value and Konditional values over a range of radii. If the points lie above the red line (expected pattern) then localisation is indicated for that radius, if the points lie below the red line then dispersion is indicated. As seen in the following plot Konditional is able to correctly identify localisation between tumour_cells and cd8_t_cells in the simulated image for a certain range of radii. When the radius gets too large the overall relationship tumour_cells and cd8_t_cells looks dispersed. The original L-function is not able to identify localisation at any value of radii.

rsDf = rsCurve(
    conditionalImage,
    from = "cd8_t_cells",
    to = "tumour_cells",
    parent = c("cd8_t_cells", "t_cells"),
    rs = seq(0.01, 0.15, 0.01),
    cores = 40
)

ggplotRs(rsDf)

6 Session Info

sessionInfo()
#> R version 4.2.1 (2022-06-23)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Debian GNU/Linux 11 (bullseye)
#> 
#> Matrix products: default
#> BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
#> LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.13.so
#> 
#> locale:
#>  [1] LC_CTYPE=C.UTF-8       LC_NUMERIC=C           LC_TIME=C.UTF-8       
#>  [4] LC_COLLATE=C           LC_MONETARY=C.UTF-8    LC_MESSAGES=C.UTF-8   
#>  [7] LC_PAPER=C.UTF-8       LC_NAME=C              LC_ADDRESS=C          
#> [10] LC_TELEPHONE=C         LC_MEASUREMENT=C.UTF-8 LC_IDENTIFICATION=C   
#> 
#> attached base packages:
#> [1] stats     graphics  grDevices utils     datasets  methods   base     
#> 
#> other attached packages:
#>  [1] plotly_4.10.0        lubridate_1.8.0      forcats_0.5.2       
#>  [4] stringr_1.4.1        dplyr_1.0.9          purrr_0.3.4         
#>  [7] readr_2.1.2          tidyr_1.2.1          tibble_3.1.8        
#> [10] ggplot2_3.3.6        tidyverse_1.3.2.9000 BiocStyle_2.24.0    
#> [13] Statial_0.0.1       
#> 
#> loaded via a namespace (and not attached):
#>   [1] utf8_1.2.2                  R.utils_2.12.0             
#>   [3] tidyselect_1.1.2            lme4_1.1-30                
#>   [5] htmlwidgets_1.5.4           ranger_0.14.1              
#>   [7] grid_4.2.1                  BiocParallel_1.30.3        
#>   [9] devtools_2.4.4              DropletUtils_1.16.0        
#>  [11] munsell_0.5.0               codetools_0.2-18           
#>  [13] miniUI_0.1.1.1              withr_2.5.0                
#>  [15] spatstat.random_2.2-0       colorspace_2.0-3           
#>  [17] Biobase_2.56.0              ggfortify_0.4.14           
#>  [19] highr_0.9                   knitr_1.40                 
#>  [21] rstudioapi_0.14             stats4_4.2.1               
#>  [23] SingleCellExperiment_1.18.0 robustbase_0.95-0          
#>  [25] tensor_1.5                  labeling_0.4.2             
#>  [27] emmeans_1.8.1-1             MatrixGenerics_1.8.1       
#>  [29] GenomeInfoDbData_1.2.8      polyclip_1.10-0            
#>  [31] farver_2.1.1                datawizard_0.6.0           
#>  [33] pheatmap_1.0.12             rhdf5_2.40.0               
#>  [35] rprojroot_2.0.3             TH.data_1.1-1              
#>  [37] coda_0.19-4                 vctrs_0.4.1                
#>  [39] generics_0.1.3              xfun_0.31                  
#>  [41] R6_2.5.1                    GenomeInfoDb_1.32.4        
#>  [43] locfit_1.5-9.6              concaveman_1.1.0           
#>  [45] bitops_1.0-7                rhdf5filters_1.8.0         
#>  [47] spatstat.utils_2.3-1        cachem_1.0.6               
#>  [49] DelayedArray_0.22.0         scam_1.2-13                
#>  [51] assertthat_0.2.1            promises_1.2.0.1           
#>  [53] scales_1.2.1                multcomp_1.4-20            
#>  [55] gtable_0.3.1                beachmat_2.12.0            
#>  [57] processx_3.7.0              goftest_1.2-3              
#>  [59] sandwich_3.0-2              robustlmm_3.0-4            
#>  [61] rlang_1.0.5                 splines_4.2.1              
#>  [63] lazyeval_0.2.2              spatstat.geom_2.4-0        
#>  [65] BiocManager_1.30.18         yaml_2.3.5                 
#>  [67] abind_1.4-5                 crosstalk_1.2.0            
#>  [69] httpuv_1.6.5                tools_4.2.1                
#>  [71] usethis_2.1.6               bookdown_0.29              
#>  [73] SpatialExperiment_1.6.1     ellipsis_0.3.2             
#>  [75] spatstat.core_2.4-4         jquerylib_0.1.4            
#>  [77] RColorBrewer_1.1-3          BiocGenerics_0.42.0        
#>  [79] sessioninfo_1.2.2           Rcpp_1.0.9                 
#>  [81] sparseMatrixStats_1.8.0     zlibbioc_1.42.0            
#>  [83] lisaClust_1.5.6             RCurl_1.98-1.8             
#>  [85] ps_1.7.1                    prettyunits_1.1.1          
#>  [87] rpart_4.1.16                deldir_1.0-6               
#>  [89] urlchecker_1.0.1            sfsmisc_1.1-13             
#>  [91] zoo_1.8-11                  S4Vectors_0.34.0           
#>  [93] SummarizedExperiment_1.26.1 fs_1.5.2                   
#>  [95] magrittr_2.0.3              data.table_1.14.2          
#>  [97] magick_2.7.3                lmerTest_3.1-3             
#>  [99] mvtnorm_1.1-3               matrixStats_0.62.0         
#> [101] pkgload_1.3.0               hms_1.1.2                  
#> [103] evaluate_0.16               mime_0.12                  
#> [105] fftwtools_0.9-11            xtable_1.8-4               
#> [107] jpeg_0.1-9                  IRanges_2.30.1             
#> [109] gridExtra_2.3               MuMIn_1.47.1               
#> [111] compiler_4.2.1              crayon_1.5.2               
#> [113] minqa_1.2.4                 R.oo_1.25.0                
#> [115] htmltools_0.5.3             tzdb_0.3.0                 
#> [117] mgcv_1.8-40                 later_1.3.0                
#> [119] tiff_0.1-11                 DBI_1.1.3                  
#> [121] tweenr_2.0.2                MASS_7.3-58.1              
#> [123] boot_1.3-28                 Matrix_1.5-1               
#> [125] cli_3.4.0                   R.methodsS3_1.8.2          
#> [127] parallel_4.2.1              insight_0.18.4             
#> [129] GenomicRanges_1.48.0        pkgconfig_2.0.3            
#> [131] numDeriv_2016.8-1.1         scuttle_1.6.3              
#> [133] spatstat.sparse_2.1-1       xml2_1.3.3                 
#> [135] roxygen2_7.2.1              bslib_0.4.0                
#> [137] dqrng_0.3.0                 XVector_0.36.0             
#> [139] estimability_1.4.1          snakecase_0.11.0           
#> [141] callr_3.7.2                 digest_0.6.29              
#> [143] parameters_0.18.2           fastGHQuad_1.0.1           
#> [145] janitor_2.1.0               spatstat.data_2.2-0        
#> [147] rmarkdown_2.16              edgeR_3.38.4               
#> [149] DelayedMatrixStats_1.18.0   spicyR_1.9.3               
#> [151] shiny_1.7.2                 EBImage_4.38.0             
#> [153] rjson_0.2.21                nloptr_2.0.3               
#> [155] lifecycle_1.0.2             nlme_3.1-159               
#> [157] jsonlite_1.8.2              Rhdf5lib_1.18.2            
#> [159] desc_1.4.2                  viridisLite_0.4.1          
#> [161] limma_3.50.3                fansi_1.0.3                
#> [163] pillar_1.8.1                spatstat.linnet_2.3-2      
#> [165] lattice_0.20-45             DEoptimR_1.0-11            
#> [167] survival_3.4-0              fastmap_1.1.0              
#> [169] httr_1.4.4                  pkgbuild_1.3.1             
#> [171] glue_1.6.2                  remotes_2.4.2              
#> [173] bayestestR_0.13.0           spatstat_2.3-4             
#> [175] png_0.1-7                   sass_0.4.2                 
#> [177] performance_0.9.2           ggforce_0.3.4              
#> [179] class_7.3-20                stringi_1.7.8              
#> [181] profvis_0.3.7               HDF5Array_1.24.2           
#> [183] memoise_2.0.1